MathModDB Ontology and Knowledge Graph for Mathematical Models
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MathModDB Ontology and Knowledge Graph for Mathematical Models

This version:
https://mardi4nfdi.de/mathmoddb/0.8.0
Revision:
0.8.0
Issued on:
2025-01-20
Authors:
Aurela Shehu, Weierstrass Institute Berlin for Applied Analysis and Stochastics
Björn Schembera, Universität Stuttgart
Burkhard Schmidt, Weierstrass Institute Berlin for Applied Analysis and Stochastics
Christine Biedinger, Fraunhofer Institute for Industrial Mathematics ITWM
Jochen Fiedler, Fraunhofer Institute for Industrial Mathematics ITWM
Marco Reidelbach, Zuse Institute Berlin
Thomas Koprucki, Weierstrass Institute Berlin for Applied Analysis and Stochastics
Publisher:
Mathematical Research Data Initiative (MaRDI, https://www.mardi4nfdi.de)
See also:
https://doi.org/10.1007/978-3-031-65990-4_14
https://doi.org/10.48550/arXiv.2408.10003
https://doi.org/10.52825/cordi.v1i.255
Download serialization:
JSON-LD RDF/XML N-Triples TTL
License:
https://creativecommons.org/licenses/by/4.0/
Visualization:
Visualize with WebVowl
Cite as:
Shehu, A., Schembera, B., Schmidt, B., Biedinger, C., Fiedler, J., Reidelbrach, M., Koprucki, T. (2025): MathModDB Ontology and Knowledge Graph for Mathematical Models
Provenance of this page
Ontology Specification Draft

Abstract

MathModDB is a database of mathematical models developed by the Mathematical Research Data Initiative (MaRDI). MathModDB defines a data model with classes (Mathematical Model, Mathematical Formulation, Research Field, Research Problem, Quantity [Kind], [Computational] Task, Publication), object properties/relations, data properties and annotation properties as an ontology. This ontology is populated with individuals/data from various fields of applied mathematics, making it a knowledge graph.

Introduction back to ToC

Motivation & Introduction

Proper documentation and storage of research data, adhering to FAIR principles, are crucial for reproducibility and scientific integrity. Applied mathematics, producing diverse numerical and symbolic data, heavily relies on models that must be well-documented for replication and future use target=”_blank”. Here, we present MathModDB, an ontology for mathematical models, along with a knowledge graph containing. The work is conducted within the NFDI project Mathematical Research Data Initiative (MaRDI).

Structure

The ontology consists of the classes Mathemical Model, Mathemical Formulation, [Computational] Task, Quantity [Kind], Research Field and Research Problem. The structure of the ontology, in conjunction with the neighboring knowledge graph for mathematical algorithms MathAlgoDB is display in the image below

Structure of MathModDB

The classes have the following semantics:
Mathematical Model A mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions. The aim of modeling is to make a particular part or feature of the world easier to simulate, interpret and/or optimize based on existing knowledge.
Research Field A field of research (or academic discipline), e.g. Arts & Humanities, Life Sciences & Biomedicine, Physical & Natural Sciences or Engineering.
Research Problem A research problem (or research question) to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research.
Mathematical Formulation Typically, a mathematical formulation is based on equations (general construct indicating equality of quantities) or on inequalities (non-equal relations between quantities), or a logic quantifier
Quantity A quantity is a property of a system that can be measured or obtained from calculation/simulation. Can be a scalar, a vector, a matrix or a higher-order tensor. The overarching, abstract quantity in the QuantityKind class should be referenced if possible/applicable.
Quantity Kind The kind of quantity, e.g. the abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, .... Note that the kind of a quantity cannot be generalized by another (kind of a) quantity.
Task A specific task associated with a mathematical model. The subclasses of this superclass should reflect their differences, e.g. a computational task or a task of doing a mathematical analysis (the latter is not yet implemented).
Computational Task A specific computational task associated with a mathematical model. Typically, various tasks differ from each other by the choice of given quantities (input), unknown quantities (output), parameters or constants as well as boundary conditions, initial conditions and/or final conditions.

MathModDB Ontology: Overview back to ToC

This ontology has the following classes and properties.

Classes

Object Properties

Data Properties

Annotation Properties

Named Individuals

MathModDB Ontology: Description back to ToC

This is the MathModDB Ontology for documenting mathematical models.

Cross-reference for MathModDB Ontology classes, object properties and data properties back to ToC

This section provides details for each class and property defined by MathModDB Ontology.

Classes

Computational Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComputationalTask

specific computational task associated with a mathematical model
has super-classes
Task c
is in domain of
applies model op, approximated by task op, approximates task op, contained in task op, contains assumption op, contains boundary condition op, contains constant op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains input op, contains objective op, contains output op, contains parameter op, contains task op, discretized by task op, discretizes task op, documented in op, generalized by task op, generalizes task op, invented in op, is linear dp, linearized by task op, linearizes task op, similar to task op, studied in op, surveyed in op, used in op
is in range of
applied by task op, approximated by task op, approximates task op, contained as assumption in op, contained as boundary condition in op, contained as constant in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in task op, contains task op, discretized by task op, discretizes task op, documents op, generalized by task op, generalizes task op, invents op, linearized by task op, linearizes task op, similar to task op, studies op, surveys op, uses op
has members
Balanced Truncation ni, Balanced Truncation (Bi-linear) ni, Balanced Truncation (Linear) ni, Calculation of Deformation and Concentration ni, Classical Time Evolution ni, Control System Time Evolution ni, Control System Time Evolution (Bi-linear) ni, Control System Time Evolution (Linear) ni, Denoising for Improved Parametric MRI of the Kidney ni, Extract Logical Rules ni, Far Field Radiation ni, Free Fall Determine Gravitation ni, Free Fall Determine Time ni, Free Fall Determine Velocity ni, H2 Optimal Approximation ni, H2 Optimal Approximation (Bi-linear) ni, H2 Optimal Approximation (Linear) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation of Enzyme Kinetics ni, Mathematical Analysis of DHW Equation ni, Maximizing Poisson log-Likelihood ni, Maximum Likelihood Estimation ni, Model Order Reduction ni, Near Field Radiation ni, Nonlinear Parameter Estimation (Uni Uni Reaction with Product - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation of Enzyme Kinetics ni, Optimal Control ni, Parameter Estimation of Enzyme Kinetics ni, Quantum Conditional Quasi-Solvability ni, Quantum Stationary States ni, Quantum Time Evolution ni, Romanization Parameter Estimation ni, Romanization Time Evolution ni, Semiconductor Charge Neutrality ni, Semiconductor Current Voltage ni, Semiconductor Thermal Equilibrium ni, Sensitivity Analysis of Complex Kinetic Systems ni, Simulation of Complex Kinetic Systems ni, Simulation of TEM Images ni, Sorting Objects ni, Symmetry Analysis In TEM Images ni
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Mathematical Formulationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalFormulationDefinition

typically, an equation (general construct indicating equality of quantities) or an inequality (non-equal relations between quantities), or a logic quantifier
is in domain of
approximated by formulation op, approximates formulation op, contained as assumption in op, contained as boundary condition in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contains assumption op, contains boundary condition op, contains constant op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains quantity op, defines op, defining formulation dp, discretized by formulation op, discretizes formulation op, documented in op, formulation property dp, generalized by formulation op, generalizes formulation op, in defining formulation dp, invented in op, is convex dp, is deterministic dp, is dimensionless dp, is dynamic dp, is linear dp, is space-continuous dp, is time-continuous dp, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, similar to formulation op, studied in op, surveyed in op, used in op
is in range of
approximated by formulation op, approximates formulation op, contained as assumption in op, contained as boundary condition in op, contained as constant in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained in formulation op, contains assumption op, contains boundary condition op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, defined by op, discretized by formulation op, discretizes formulation op, documents op, generalized by formulation op, generalizes formulation op, invents op, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, similar to formulation op, studies op, surveys op, uses op
has members
Active Contractile Force (Definition) ni, Allee Effect ni, Ampere Law ni, Anharmonicity Constant (Definition) ni, Attraction Force At Opinion Formulation ni, Average Opinion Of Followers Of Infuencers Formulation ni, Average Opinion Of Followers Of Infuencers In The Partial Mean Field Model Formulation ni, Average Opinion Of Followers Of Media Formulation ni, Average Opinion Of Followers Of Media In The Partial Mean Field Model Formulation ni, Balancing Transformation ni, Beavers–Joseph-Saffman Condition ni, Between Population Contact Rate Equation ni, Bi Bi Reaction Ordered Mechanism ODE System ni, Bi Bi Reaction Ordered Mechanism with single central Complex ODE System ni, Bi Bi Reaction Ping Pong Mechanism ODE System ni, Bi Bi Reaction Theorell-Chance Mechanism ODE System ni, Binary Decision Variable (Definition) ni, Boltzmann Approximation For Electrons ni, Boltzmann Approximation For Holes ni, Boundary Conditions of Electrophysiological Muscle ODE System ni, Change In Opinions Of Individuals ni, Change In Opinions Of Influencers ni, Change In Opinions Of Influencers In The Partial Mean Field Model ni, Change In Opinions Of Media ni, Change In Opinions Of Media In The Partial Mean Field Model ni, Classical Approximation ni, Classical Brownian Equation ni, Classical Fokker Planck Equation ni, Classical Hamilton Equations ni, Classical Hamilton Equations (Leap Frog) ni, Classical Langevin Equation ni, Classical Liouville Equation ni, Classical Momentum (Definition) ni, Classical Newton Equation ni, Classical Newton Equation (Stoermer Verlet) ni, Closed System Approximation ni, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition) ni, Condition For Positive Solutions In The Multi-Population SI Model ni, Condition For Positive Solutions In The Multi-Population SIR Model ni, Condition For Positive Solutions In The Multi-Population SIS Model ni, Condition For Positive Solutions In The SIR Model ni, Condition For Positive Solutions In The SIR Model with Births and Deaths ni, Condition For Positive Solutions In The SIS Model ni, Condition For Positive Solutions In The SIS Model with Births and Deaths ni, Condition To Keep Susceptibles Positive ni, Conservation Law ni, Conservation of City Numbers ni, Constant Population Size ni, Contact Network (Definition) ni, Contact Network (Time-dependent, Definition) ni, Contact Network Constraint ni, Continuity Equation ni, Continuity Equation For Electrons ni, Continuity Equation For Electrons (Finite Volume) ni, Continuity Equation For Holes ni, Continuity Equation For Holes (Finite Volume) ni, Continuity of the Normal Mass Flux ni, Continuity of the Normal Stresses ni, Continuous Rate of Change of Infectious in the SI Model ni, Continuous Rate of Change of Infectious in the SIR Model ni, Continuous Rate of Change of Removed in the SIR Model ni, Continuous Rate of Change of Susceptibles in the SI Model ni, Continuous Rate of change of Infectious in the SIS Model ni, Continuous Rate of change of Susceptibles in the SIR Model ni, Continuous Rate of change of Susceptibles in the SIS Model ni, Control System Initial (Reduced) ni, Control System Input Bilinear ni, Control System Input Bilinear (Reduced) ni, Control System Input Linear ni, Control System Input Linear (Reduced) ni, Control System Matrix A (Reduced, Definition) ni, Control System Matrix B (Reduced, Definition) ni, Control System Matrix C (Reduced, Definition) ni, Control System Matrix D (Reduced, Definition) ni, Control System Matrix N (Reduced, Definition) ni, Control System Output Linear ni, Control System Output Linear (Reduced) ni, Control System Output Quadratic ni, Control System Output Quadratic (Reduced) ni, Control System State (Reduced, Definition) ni, Control Volume (Definition) ni, Coulomb Friction Of Two Particles ni, Darcy Equation ni, Darcy Equation (Euler Backward) ni, Darcy Equation (Finite Volume) ni, Darwin-Howie-Whelan Equation for a strained crystal ni, Darwin-Howie-Whelan Equation for an unstrained crystal ni, Detailed Balance Principle ni, Dirichlet Boundary Condition ni, Dirichlet Boundary Condition For Electric Potential ni, Dirichlet Boundary Condition For Electron Fermi Potential ni, Dirichlet Boundary Condition For Hole Fermi Potential ni, Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Electric Current Density Of Electrons (Definition) ni, Electric Current Density Of Holes (Definition) ni, Electrophysiological Muscle ODE System ni, Empirical Distribution Of Individuals Formulation ni, Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme Concentration ODE (Bi Bi Reaction Ping Pong) ni, Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme Concentration ODE (Uni Uni Reaction) ni, Enzyme Conservation ni, Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition) ni, Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Euler Backward Method ni, Euler Forward Method ni, Excess Substrate Assumption ni, Expectation Value (Quantum Density, Definition) ni, Expectation Value (Quantum State, Definition) ni, Faraday Law ni, Fick Equation ni, Finite Volume Method ni, Fourier Equation ni, Fraction Of Population Density Of Exposed Formulation ni, Fraction Of Population Density Of Infectious Formulation ni, Fraction Of Population Density Of Susceptibles Formulation ni, Free Fall Equation (Air Drag) ni, Free Fall Equation (Non-Uniform Gravitation) ni, Free Fall Equation (Vacuum) ni, Free Fall Initial Condition ni, Free Fall Terminal Velocity (Definition) ni, Free Fall Time (Definition) ni, Gamma-Gompertz–Makeham Law ni, Gauss Law (Electric Field) ni, Gauss Law (Magnetic Field) ni, Gaussian Distribution (Definition) ni, Gompertz Law ni, Gompertz–Makeham Law ni, Gramian Generalized Controllability (Definition) ni, Gramian Generalized Observability (Definition) ni, Gramian Matrix Controllability (Definition) ni, Gramian Matrix Observability (Definition) ni, Graph Type Identifier (Definition) ni, Gravitational Acceleration (Earth Surface, Definition) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Hill-Type Two-Muscle-One-Tendon ODE System ni, Homogeneous Neumann Boundary Conditions ni, Hooke Law (Linear Elasticity) ni, Hooke Law (Spring) ni, Infectious At Time Step n+1 in The SIS Model ni, Infectious At Time Step n+1 in The SIS Model with births and deaths ni, Infectious At Time Step n+1 in the Multi-Population SI Model ni, Infectious At Time Step n+1 in the Multi-Population SIR Model ni, Infectious At Time Step n+1 in the Multi-Population SIS Model ni, Infectious At Time Step n+1 in the SI Model ni, Infectious At Time Step n+1 in the SIR Model ni, Infectious At Time Step n+1 in the SIR Model with Births and Deaths ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Initial Classical Density ni, Initial Classical Momentum ni, Initial Classical Position ni, Initial Classical Velocity ni, Initial Condition for the Multi-Population SI Model ni, Initial Condition for the Multi-Population SIS Model ni, Initial Condition For The Discrete SIR Model with and without Births and Deaths ni, Initial Condition for the Continuous SI Model and SIS Model ni, Initial Condition for the Continuous SIR Model ni, Initial Condition for the Discrete SI Model ni, Initial Condition for the Multi-Population SIR Model ni, Initial Control State ni, Initial Control State (Reduced, Definition) ni, Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni, Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni, Initial Inhibitor Concentration (Uni Uni Reaction) ni, Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Number Of Infected Cities ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni, Initial Product Concentration (Uni Uni Reaction - ODE Model) ni, Initial Product Concentration (Uni Uni Reaction with Product) ni, Initial Product Concentration (Uni Uni Reaction without Product) ni, Initial Quantum Density ni, Initial Quantum State ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni, Initial Substrate Concentration (Uni Uni Reaction) ni, Initial Value For Electron Scattering ni, Integral Of The Population Density Fraction Of Exposed (Initial Condition) ni, Integral Of The Population Density Fraction Of Infectious (Initial Condition) ni, Integral Of The Population Density Fraction Of Susceptibles (Initial Condition) ni, Integral Of The Total Population Density (Initial Condition) ni, Interaction Force On An Individual ni, Interaction Weight Between Individuals ni, Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni, Intermediate Concentration ODE (Bi Bi Reaction Ping Pong) ni, Irreversibility Assumption ni, Isotropic Gaussian Function Formulation ni, Laplace Equation For The Electric Potential ni, Limiting Distribution Of Individuals Formulation ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition) ni, Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition) ni, Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni, Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni, Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition) ni, Line Concept ni, Line Concept Costs ni, Line Costs Computation ni, Linear Strain (Definition) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Liouville-von Neumann Equation ni, Logical Rule Extraction Formulation ni, Lorentz Force Equation (Non-Relativistic) ni, Lorentz Force Equation (Relativistic) ni, Loss Function (Definition) ni, Loss Function Minimization ni, Lumped Activation Parameter ni, Lyapunov Equation ni, Lyapunov Equation Controllability ni, Lyapunov Equation Observability ni, Lyapunov Generalized Controllability ni, Lyapunov Generalized Observability ni, Mass Action Law ni, Mass Balance Law ni, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition) ni, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition) ni, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered without Products - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered without Products and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance without Products - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction with Product - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni, Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni, Molecular Alignment ni, Molecular Orientation ni, Momentum Balance Equation ni, Monodomain Equation for Action Potential Propagation ni, Motor Neuron Pool ODE System ni, Neumann Boundary Condition ni, Neumann Boundary Condition (Stress-Free Relaxation) ni, Neumann Boundary Condition For Electric Potential ni, Neumann Boundary Condition For Electron Fermi Potential ni, Neumann Boundary Condition For Hole Fermi Potential ni, Neumann Boundary Condition For SEIR Model ni, Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni, Non-Local Means ni, Nonrelativistic Approximation ni, Normal Interaction Force Of Two Particles ni, Normal Mode Coordinate (Dimensionless, Definition) ni, Normal Mode Momentum (Dimensionless, Definition) ni, Number Of Exposed Individuals Formulation ni, Number Of Individuals Tends To Infinity Assumption ni, Number Of Susceptible Individuals Formulation ni, Object Cluster Formulation ni, Object Committor Function Formulation ni, Object Commonality Formulation ni, Object Comparison Formulation ni, Object Rating Formulation ni, Object Rating Matrix Decomposition (Schur) ni, Ohm Equation ni, Optimal Control Backward ni, Optimal Control Constraint ni, Optimal Control Cost (Definition) ni, Optimal Control Final ni, Optimal Control Forward ni, Optimal Control Initial ni, Optimal Control Target (Definition) ni, Optimal Control Update ni, Overall Distribution Of Individuals Formulation ni, Pair Function Assumption ni, Passive Muscle Force (Definition) ni, Passive Tendon Force (Definition) ni, Periodic Boundary Condition For Electric Potential ni, Periodic Boundary Conditions ni, Permittivity (Relative, Definition) ni, Poisson Distribution (Definition) ni, Poisson Equation For The Electric Potential ni, Poisson Equation For The Electric Potential (Finite Volume) ni, Poisson log-Likelihood ni, Poisson-Distributed Deaths ni, Poro-Visco-Elastic (Dirichlet Boundary) ni, Poro-Visco-Elastic (Neumann Boundary) ni, Poro-Visco-Elastic Diffusion Boundary Condition ni, Poro-Visco-Elastic Diffusion Equation ni, Poro-Visco-Elastic Quasistatic Equation ni, Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Product 1 Concentration ODE (Bi Bi Reaction Ordered) ni, Product 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Product 2 Concentration ODE (Bi Bi Reaction Ordered) ni, Product 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Product Concentration ODE (Uni Uni Reaction) ni, Public Transportation Network ni, Quantum Eigen Energy (Anharmonic) ni, Quantum Eigen Energy (Harmonic) ni, Quantum Eigen Energy (Intermolecular) ni, Quantum Hamiltonian (Electric Charge) ni, Quantum Hamiltonian (Electric Dipole) ni, Quantum Hamiltonian (Electric Polarizability) ni, Quantum Hamiltonian (Linear Rotor) ni, Quantum Hamiltonian (Non-Rigid Rotor) ni, Quantum Hamiltonian (Normal Mode) ni, Quantum Hamiltonian (Normal Mode, Anharmonic) ni, Quantum Hamiltonian (Normal Mode, Harmonic) ni, Quantum Hamiltonian (Normal Mode, Intermolecular) ni, Quantum Hamiltonian (Symmetric Top) ni, Quantum Jump Operator (Definition) ni, Quantum Lindblad Equation ni, Quantum Momentum Operator (Definition) ni, Rapid Equilibrium Assumption ni, Rate Of Change Of Population Density Fraction Of Exposed PDE ni, Rate Of Change Of Population Density Fraction Of Infectious PDE ni, Rate Of Change Of Population Density Fraction Of Removed PDE ni, Rate Of Change Of Population Density Fraction Of Susceptibles PDE ni, Rate Of Switching Influencers Formulation ni, Relativistic Momentum (Definition) ni, Removed At Time Step n+1 in The Multi-Population Discrete SIR Model ni, Removed At Time Step n+1 in the Discrete SIR Model ni, Removed At Time Step n+1 in the Discrete SIR Model with Births and Deaths ni, Runge–Kutta Method ni, SEIR Derivative Relation ni, Schrödinger Equation (Chebychev Polynomial) ni, Schrödinger Equation (Differencing Scheme) ni, Schrödinger Equation (Lie-Trotter) ni, Schrödinger Equation (Second Order Differencing) ni, Schrödinger Equation (Split Operator) ni, Schrödinger Equation (Strang-Marchuk) ni, Schrödinger Equation (Time Dependent) ni, Schrödinger Equation (Time Independent) ni, Schrödinger-Newton Equation ni, Second Condition For Positive Solutions In The Multi Population SIS Model ni, Second Condition For Positive Solutions In The SIR Model with Births and Deaths ni, Second Condition For Positive Solutions In The SIS Model ni, Second Condition For Positive Solutions In The SIS Model with Births and Deaths ni, Sensory Organ ni, Solar System Equations Of Motion ni, Speed Of Light (Definition) ni, Spherical Harmonics Expansion (3D) ni, Spreading Curve (Approximate, Formulation) ni, Spreading Rate (Time-dependent) Constraint ni, Stability Autonomous System ni, Steady State Assumption ni, Stokes Darcy Coupling Conditions ni, Stokes Darcy Equation (Discretized, pv) ni, Stokes Darcy Equation (Discretized, td) ni, Stokes Equation ni, Stokes Equation (Euler Backward) ni, Stokes Equation (Finite Volume) ni, Subcellular DAE System ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ordered) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Substrate Concentration ODE (Uni Uni Reaction) ni, Susceptible Cities ODE ni, Susceptible Infectious Epidemic Spreading ODE System ni, Susceptibles At Time Step n +1 in the Discrete Multi Population SI Model ni, Susceptibles At Time Step n +1 in the Discrete Multi Population SIR Model ni, Susceptibles At Time Step n +1 in the Discrete Multi Population SIS Model ni, Susceptibles At Time Step n+1 in The Discrete SI Model ni, Susceptibles At Time Step n+1 in The Discrete SIR Model ni, Susceptibles At Time Step n+1 in The Discrete SIS Model ni, Susceptibles At Time Step n+1 in The Discrete SIS Model with births and deaths ni, Susceptibles At Time Step n+1 in the Discrete SIR Model with births and deaths ni, Sylvester Equation ni, Sylvester Equation Controllability ni, Sylvester Equation Observability ni, Sylvester Generalized Controllability ni, Sylvester Generalized Observability ni, Tangential Interaction Force Of Two Particles ni, Tendon Strain (Definition) ni, Time Independence Of Hamiltonian ni, Torque Of Particle ni, Total Population Density Formulation ni, Transport Equation ni, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition) ni, Uni Uni Reaction ODE System ni, Uniform Gravitational Acceleration ni, Vanishing Air Density ni, Vanishing Drag Coefficient ni, Vibrational Frequency Shift (1st Order) ni, Vibrational Frequency Shift (2nd Order) ni, Weight Factor (Definition) ni, Young Modulus (Definition) ni, de Broglie Wavelength (Definition) ni
is disjoint with
Computational Task c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Mathematical Modelc back to ToC or Class ToC

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a mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions
is in domain of
applied by task op, approximated by model op, approximates model op, contained in model op, contains assumption op, contains boundary condition op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains model op, discretized by model op, discretizes model op, documented in op, generalized by model op, generalizes model op, invented in op, is convex dp, is deterministic dp, is dimensionless dp, is dynamic dp, is linear dp, is space-continuous dp, is time-continuous dp, linearized by model op, linearizes model op, models op, similar to model op, studied in op, surveyed in op, used in op
is in range of
applies model op, approximated by model op, approximates model op, contained as assumption in op, contained as boundary condition in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained in model op, contains model op, discretized by model op, discretizes model op, documents op, generalized by model op, generalizes model op, invents op, linearized by model op, linearizes model op, modeled by op, similar to model op, studies op, surveys op, uses op
has members
Action Potential Propagation Model ni, Artificial Neural Network ni, Bi Bi Reaction Ordered Mechanism (ODE Model) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism with single central Complex (ODE Model) ni, Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism (ODE Model) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Charge Transport Model ni, Classical Brownian Model ni, Classical Dynamics Model ni, Classical Fokker Planck Model ni, Classical Langevin Model ni, Continuous Susceptible Infectious Model ni, Continuous Susceptible Infectious Removed Model ni, Continuous Susceptible Infectious Susceptible Model ni, Control System Model ni, Control System Model (Bilinear) ni, Control System Model (Linear) ni, Darcy Model ni, Darcy Model (Discretized) ni, Diffusion Model ni, Discrete Element Method ni, Discrete Susceptible Infectious Model ni, Discrete Susceptible Infectious Removed Model ni, Discrete Susceptible Infectious Susceptible Model ni, Drift-Diffusion Model ni, Dynamical Electron Scattering Model ni, Electron Shuttling Model ni, Electrophysiological Muscle Model ni, Feedforward Neural Network ni, Free Fall Model (Air Drag) ni, Free Fall Model (Non-Uniform Gravitation) ni, Free Fall Model (Vacuum) ni, Gamma-Gompertz-Makeham Model ni, Gaussian Noise Model ni, Heat Conduction Model ni, Hill-Type Two-Muscle-One-Tendon Model ni, Linear Discrete Element Method ni, Linear Rotor ni, Linear Rotor (Apolar) ni, Linear Rotor (Combined) ni, Linear Rotor (Non-Rigid) ni, Linear Rotor (Polar) ni, Lorentz Force Model (Non-Relativistic) ni, Lorentz Force Model (Relativistic) ni, Loss Function ni, Maxwell Equations Model ni, Motor Neuron Pool Model ni, Multi-Population Discrete Susceptible Infectious Model ni, Multi-Population Discrete Susceptible Infectious Removed Model ni, Multi-Population Discrete Susceptible Infectious Susceptible Model ni, Multipolar Expansion Model (3D) ni, Normal Modes ni, Normal Modes (Anharmonic) ni, Normal Modes (Harmonic) ni, Normal Modes (Intermolecular) ni, Object Comparison Model ni, Opinion Model With Influencers And Media ni, PDE SEIR Model ni, Partial Mean Field Opinion Model ni, Poro-Visco-Elastic Model ni, Quantum Classical Model ni, Quantum Model (Closed System) ni, Quantum Model (Open System) ni, Recurrent Neural Network ni, Recurrent Neural Network Surrogate for Discrete Element Method ni, Scharfetter-Gummel Scheme ni, Sensory Organ Model ni, Solar System Model ni, Stokes Darcy Model ni, Stokes Darcy Model (Discretized) ni, Stokes Model ni, Stokes Model (Discretized) ni, Subcellular Model ni, Susceptible Infectious Epidemic Spreading Model ni, Susceptible Infectious Removed Model with Births and Deaths ni, Susceptible Infectious Susceptible Model with Births and Deaths ni, Symmetric Top (Combined) ni, Transport Model ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction (ODE Model) ni, Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
is disjoint with
Computational Task c, Mathematical Formulation c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Publicationc back to ToC or Class ToC

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publication that reports original empirical and theoretical work in the sciences
is in domain of
documents op, invents op, studies op, surveys op, uses op
is in range of
documented in op, invented in op, studied in op, surveyed in op, used in op
has members
Allen (1993) Some Discrete-Time SI, SIR and SIS Epidemic Models ni, Bisswanger (2017) Enzyme Kinetics ni, Briggs (1925) A note on the kinetics of enzyme action ni, Cundall (1979) A discrete numerical model for granular assemblies ni, Eadie (1942) The Inhibition of Cholinesterase by Physostigmine and Prostigmine ni, Ermoneit (2023) Optimal control of conveyor-mode spin-qubit shuttling in a Si/SiGe quantum bus in the presence of charged defects ni, Gattermann (2017) Line pool generation ni, Hanes (1932) Studies on plant amylases: The effect of starch concentration upon the velocity of hydrolysis by the amylase of germinated barley ni, Helfmann (2023) Modelling opinion dynamics under the impact of influencer and media strategies ni, Hofstee (1959) Non-inverted versus inverted plots in enzyme kinetics ni, Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni, Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni, Koprucki (2017) Numerical methods for drift-diffusion models ni, Kostré (2022) Understanding the romanization spreading on historical interregional networks in Northern Tunisia ni, Leskovac (2003) Comprehensive Enzyme Kinetics ni, Lineweaver (1934) The Determination of Enzyme Dissociation Constants ni, Michaelis (1913) Die Kinetik der Invertinwirkung ni, Oosterhout (2024) Finite-strain poro-visco-elasticity with degenerate mobility ni, Slyke (1914) The mode of action of urease and of enzymes in general ni, Suan (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolution ni, Sylvester (1884) Sur léquations en matrices px = xq ni, Weber (2022) The Mathematics of Comparing Objects ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantityc back to ToC or Class ToC

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is in domain of
approximated by quantity op, approximates quantity op, contained as constant in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in formulation op, defined by op, documented in op, generalized by quantity op, generalizes quantity op, invented in op, is dimensionless dp, linearized by quantity op, linearizes quantity op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studied in op, surveyed in op, used in op
is in range of
approximated by quantity op, approximates quantity op, contains constant op, contains input op, contains objective op, contains output op, contains parameter op, contains quantity op, defines op, documents op, generalized by quantity op, generalizes quantity op, invents op, linearized by quantity op, linearizes quantity op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studies op, surveys op, uses op
has members
Active Contractile Force ni, Adjacency Matrix ni, Age Of An Individual ni, Allee Threshold ni, Amplitude Of Electron Wave ni, Anharmonicity Constant ni, Applied External Voltage ni, Asymptomatic Infection Rate ni, Asymptomatic Recovery Rate ni, Attraction Force At Opinion ni, Average Opinion Of Followers Of Influencers ni, Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni, Average Opinion Of Followers Of Media ni, Average Opinion Of Followers Of Media In The Partial Mean Field Model ni, Band Edge Energy For Conduction Band ni, Band Edge Energy For Valence Band ni, Beavers-Joseph Coefficient ni, Between Population Contact Rate ni, Binary Decision Variable ni, Birth Rate ni, Boltzmann Constant ni, Boolean Ring ni, Center Of Province ni, Centrifugal Distortion Constant ni, Change In Length ni, Chemical Potential ni, Classical Acceleration ni, Classical Density (Phase Space) ni, Classical Force ni, Classical Hamilton Function ni, Classical Momentum ni, Classical Position ni, Classical Velocity ni, Coefficient Scaling Infectious To Exposed ni, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni, Complexed Enzyme Concentration ni, Contact Network ni, Contact Network (Time-dependent) ni, Contact Rate ni, Contact Rate Between Two Groups ni, Control System Duration ni, Control System Initial ni, Control System Input ni, Control System Lagrange Multiplier ni, Control System Matrix A ni, Control System Matrix A (Reduced) ni, Control System Matrix B ni, Control System Matrix B (Reduced) ni, Control System Matrix C ni, Control System Matrix C (Reduced) ni, Control System Matrix D ni, Control System Matrix D (Reduced) ni, Control System Matrix N ni, Control System Matrix N (Reduced) ni, Control System Output ni, Control System State ni, Control System State (Reduced) ni, Control Volume ni, Coriolis Coupling Constant ni, Costs of Line Concept ni, Costs per Unit ni, Coupling Current ni, Cross Section ni, Current Density ni, Current Procedural Terminology ni, Death Count ni, Density Fraction Coefficient ni, Density Of Air ni, Density Of Electrons ni, Density Of Holes ni, Density Of States For Conduction Band ni, Density Of States For Valence Band ni, Diffusion Coefficient ni, Diffusion Coefficient for SEIR Model ni, Diffusion Flux ni, Dirac Delta Distribution ni, Displacement ni, Displacement Muscle Tendon ni, Displacement Of Atoms ni, Dissociation Constant ni, Doping Profile ni, Drag Coefficient ni, Drift (Velocity) ni, Duration ni, Duration per Unit ni, Earth Mass ni, Earth Radius ni, Edges ni, Effective Conductivity ni, Effective Mass ni, Effective Mass (Solid-State Physics) ni, Effective Mass (Spring-Mass System) ni, Eigenstress Of Crystal ni, Elastic Stiffness Tensor ni, Electric Charge Density ni, Electric Current Density ni, Electric Current Density Of Electrons ni, Electric Current Density Of Holes ni, Electric Potential ni, Electric Potential Fourier Coefficients ni, Electrode Interfaces ni, Electron Mass ni, Elementary Charge ni, Empirical Distribution Of Individuals ni, Enzyme - Product 1 - Product 2 Complex Concentration ni, Enzyme - Product 1 Complex Concentration ni, Enzyme - Product 2 Complex Concentration ni, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration ni, Enzyme - Substrate 1 - Substrate 2 Complex Concentration ni, Enzyme - Substrate 1 Complex Concentration ni, Enzyme Concentration ni, Enzyme-Substrate Complex Concentration ni, Equilibrium Constant ni, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni, Euler Number ni, Excitation Error ni, Expectation Value (Quantum Density) ni, Expectation Value (Quantum State) ni, Exposure Of An Individual ni, External Chemical Potential ni, External Force Density ni, Extrinsic Mortality ni, Fermi Potential For Electrons ni, Fermi Potential For Holes ni, Fiber Contraction Velocity ni, Fiber Stretch ni, Fixed Costs ni, Fluid Density ni, Fluid Dynamic Viscosity (Free Flow) ni, Fluid Dynamic Viscosity (Porous Medium) ni, Fluid Intrinsic Permeability (Porous Medium) ni, Fluid Kinematic Viscosity (Free Flow) ni, Fluid Pressure (Free Flow) ni, Fluid Pressure (Porous Medium) ni, Fluid Velocity (Free Flow) ni, Fluid Velocity (Porous Medium) ni, Fluid Viscous Stress ni, Flux Of Electrons ni, Flux Of Holes ni, Force Constant (Anharmonic) ni, Force Constant (Harmonic) ni, Force Density ni, Fraction Of Population Density Of Exposed ni, Fraction Of Population Density Of Infectious ni, Fraction Of Population Density Of Removed ni, Fraction Of Population Density Of Susceptibles ni, Free Energy Density ni, Free Fall Height ni, Free Fall Impact Time ni, Free Fall Impact Velocity ni, Free Fall Initial Height ni, Free Fall Initial Velocity ni, Free Fall Mass ni, Free Fall Terminal Velocity ni, Free Fall Time ni, Free Fall Velocity ni, Friction Coefficient ni, Gaussian Distribution ni, Gramian Generalized Controllability ni, Gramian Generalized Observability ni, Gramian Matrix ni, Gramian Matrix Controllability ni, Gramian Matrix Observability ni, Graph Type Identifier ni, Gravitational Acceleration (Earth Surface) ni, Gravitational Constant ni, Gröbner Basis ni, Hankel Singular Value ni, Heat Flux ni, Heterogeneity of Death Rate ni, Hydraulic Conductivity ni, Hyperstress Potential ni, Ideal ni, Individual Relationship Matrix ni, Inertia Parameter For Opinion Changes Of Influencers ni, Inertia Parameter For Opinion Changes Of Media ni, Infected Recovery Rate ni, Infectious ni, Influencer Individual Matrix ni, Inhibition Constant ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibitor Concentration ni, Initial Control State (Reduced) ni, Initial Reaction Rate ni, Interaction Force ni, Interaction Weight ni, Intermediate - Substrate 2 Complex Concentration ni, Intermediate Concentration ni, Intermolecular Potential ni, Ion Current ni, Isotropic Gaussian Function ni, Lagrange Multiplier ni, Length Of Unit Cell ni, Level Of Mortality ni, Likelihood Value ni, Limiting Distribution Of Individuals ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni, Limiting Reaction Rate (Uni Uni Reaction - Backward) ni, Limiting Reaction Rate (Uni Uni Reaction - Forward) ni, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni, Linear Strain ni, Link Recommendation Function ni, Loss Function ni, MOR Transformation Matrix ni, Material Density ni, Material Point Acceleration ni, Material Point Displacement ni, Material Point Velocity ni, Maximal Object Descriptiveness Rating ni, Maximum Isometric Muscle Force ni, Mechanical Deformation (Boundary Value) ni, Medium Follower Matrix ni, Medium Influencer Fraction ni, Medium Influencer Fraction Limit ni, Membrane Capacitance ni, Michaelis Constant ni, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni, Mobility Of Electrons ni, Mobility Of Holes ni, Molecularity ni, Muscle Contraction Velocity ni, Muscle Length ni, Muscle Spindle Firing Rate ni, Neural Firing Rate ni, Neural Input ni, Nodes ni, Noise Strength ni, Normal Mode Coordinate ni, Normal Mode Coordinate (Dimensionless) ni, Normal Mode Momentum ni, Normal Mode Momentum (Dimensionless) ni, Normal Stress ni, Number Of Exposed Individuals ni, Number Of Infected Cities ni, Number Of Infectious Individuals ni, Number Of Occurrences ni, Number Of Removed Individuals ni, Number Of Susceptible Cities ni, Number Of Susceptible Individuals ni, Number of Cities ni, Number of Object Properties ni, Number of Objects ni, Number of Particles ni, Number of Regions ni, Number of Time Points ni, Object Cluster Matrix ni, Object Committor Functions ni, Object Commonality Matrix ni, Object Property ni, Object Rating Matrix ni, Opinion ni, Opinion Vector of Individuals ni, Opinion Vector of Influencers ni, Opinion Vector of Media ni, Optimal Control Cost ni, Optimal Control Penalty Factor ni, Optimal Control Target ni, Origin Destination Data ni, Orthogonal Matrix ni, Overall Distribution Of Individuals ni, PTN Line ni, Pair Function ni, Parameter To Scale Attractive Force From Influencers ni, Parameter To Scale Attractive Force From Media ni, Parameter To Scale Attractive Force From Other Individuals ni, Particle Flux Density ni, Particle Number Density ni, Passive Muscle Force ni, Passive Muscle Strain ni, Passive Tendon Force ni, Period Length ni, Permeability (Vacuum) ni, Permittivity (Dielectric) ni, Permittivity (Relative) ni, Permittivity (Vacuum) ni, Pi Number ni, Planck Constant ni, Poisson Distribution ni, Population Density ni, Power Set ni, Probability Distribution ni, Product 1 Concentration ni, Product 2 Concentration ni, Product Concentration ni, Proton Mass ni, Quantile Function Of The Beta Distribution ni, Quantum Angular Momentum Operator ni, Quantum Damping Rate ni, Quantum Density Operator ni, Quantum Eigen Energy ni, Quantum Hamiltonian Operator ni, Quantum Jump Operator ni, Quantum Kinetic Operator ni, Quantum Mechanical Operator ni, Quantum Momentum Operator ni, Quantum Number ni, Quantum Potential Operator ni, Quantum State Vector ni, Quantum State Vector (Dynamic) ni, Quantum State Vector (Stationary) ni, Rate Of Aging ni, Rate Of Becoming Infectious ni, Rate Of Change Of Susceptible Cities ni, Rate Of Switching Influencers ni, Reaction Rate ni, Reaction Rate Constant ni, Reaction Rate of Enzyme ni, Reaction Rate of Enzyme - Product 1 - Product 2 Complex ni, Reaction Rate of Enzyme - Product 1 Complex ni, Reaction Rate of Enzyme - Product 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 Complex ni, Reaction Rate of Intermediate ni, Reaction Rate of Intermediate - Substrate 2 Complex ni, Reaction Rate of Product 1 ni, Reaction Rate of Product 2 ni, Reaction Rate of Substrate 1 ni, Reaction Rate of Substrate 2 ni, Reciprocal Lattice ni, Reciprocal Lattice Vectors ni, Recombination Of Electron Hole Pairs ni, Region ni, Region Connectivity ni, Relative Removal Rate ni, Relativistic Momentum ni, Removed ni, Risk Of Death ni, Romanized Cities Vector ni, Rotational Constant ni, Scaling Parameter For Switching Influencers ni, Second Eigenvalue of Orthogonal Matrix ni, Sensory Organ Current ni, Spatial Variable ni, Speed Of Light ni, Spreading Curve (Approximate) ni, Spreading Rate (Time-dependent) ni, Spring Constant ni, Stress Free Muscle Length ni, Stress Free Tendon Length ni, Stress Of Crystal ni, Stress Tensor (Cauchy) ni, Stress Tensor (Piola-Kirchhoff) ni, Substrate 1 Concentration ni, Substrate 2 Concentration ni, Substrate Concentration ni, Surface Force Density ni, Susceptibles ni, Symptomatic Infection Rate ni, Tendon Length ni, Tendon Strain ni, Thermal Conductivity ni, Time Point ni, Time Step ni, Total Number Of Individuals ni, Total Population Density ni, Total Population Size ni, Traffic Load ni, Transmembrane Potential ni, Transport Route ni, Turn Over Time ni, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni, Unit Normal Vector ni, Unit Tangent Vector ni, Unknown Matrix ni, Upper-Triangular Matrix ni, Vibration Frequency (Anharmonic) ni, Vibration Frequency (Harmonic) ni, Viscous Dissipation Potential ni, Wave Vector of an Electron ni, Weight Factor ni, White Noise ni, Wiener Process ni, Young Modulus ni, de Broglie Wavelength ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantity Kindc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantityKind

abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, ....
is in domain of
contained as constant in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in formulation op, defined by op, documented in op, generalizes quantity op, invented in op, is dimensionless dp, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studied in op, surveyed in op, used in op
is in range of
contains constant op, contains input op, contains objective op, contains output op, contains parameter op, contains quantity op, defines op, documents op, generalized by quantity op, invents op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studies op, surveys op, uses op
has members
Acceleration ni, Angular Momentum ni, Area ni, Azimuthal Angle ni, Boolean Variable ni, Complex Number (Dimensionless) ni, Concentration ni, Costs ni, Decision Variable ni, Density ni, Electric Capacitance ni, Electric Charge ni, Electric Conductivity ni, Electric Current ni, Electric Dipole Moment ni, Electric Field ni, Electric Polarizability ni, Energy ni, Expectation Value ni, Force ni, Frequency ni, Integer Number (Dimensionless) ni, Length ni, Magnetic Field ni, Mass ni, Mechanical Deformation ni, Mechanical Strain ni, Mechanical Stress ni, Momentum ni, Number (Dimensionless) ni, Object ni, Polar Angle ni, Pressure ni, Proton Electron Mass Ratio ni, Radius ni, Rate ni, Real Number (Dimensionless) ni, Temperature ni, Time ni, Torque ni, Variance ni, Velocity ni, Viscosity ni, Voltage ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Research Field c, Research Problem c, Task c

Research Problemc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ResearchProblem

problem to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research
is in domain of
contained in field op, documented in op, generalized by problem op, generalizes problem op, invented in op, modeled by op, similar to problem op, studied in op, surveyed in op, used in op
is in range of
contains problem op, documents op, generalized by problem op, generalizes problem op, invents op, models op, similar to problem op, studies op, surveys op, uses op
has members
Bi Bi Reaction ni, Bi Bi Reaction following Ordered Mechanism ni, Bi Bi Reaction following Ordered Mechanism with single central complex ni, Bi Bi Reaction following Ping Pong Mechanism ni, Bi Bi Reaction following Theorell-Chance Mechanism ni, Charge Transport ni, Current Flow in Semiconductor Devices ni, Efficient Numerical Simulation of Soil-Tool Interaction ni, Electromagnetic Fields And Waves ni, Flow in Porous Media ni, Free Flow Coupled to Porous Media Flow ni, Free Flow of an Incompressible Fluid ni, Gravitational Effects On Fruit ni, Heat Transport ni, Identify Destruction Rules in Ancient Egyptian Objects ni, Image Denoising ni, Imaging of Nanostructures ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 and 2 ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Products ni, Initial Reaction Rate of Uni Uni Reaction with Product ni, Initial Reaction Rate of Uni Uni Reaction without Product ni, Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni, Line Planning ni, Molecular Dynamics ni, Molecular Reaction Dynamics ni, Molecular Rotation ni, Molecular Spectroscopy ni, Molecular Spectroscopy (Transient) ni, Molecular Spectrosopy (Stationary) ni, Molecular Vibration ni, Mortality Modeling ni, Muscle Movement ni, Opinion Dynamics ni, Particles In Electromagnetic Fields ni, Poro-Visco-Elastic Evolution ni, Romanization Spreading in Northern Tunesia ni, Solar System Mechanics ni, Sort Ancient Egyptian Objects ni, Species Transport ni, Spin Qbit Shuttling ni, Spreading of Infectious Diseases ni, Transport of Matter ni, Uni Uni Reaction ni, Uni Uni Reaction with Competitive Complete Inhibition ni, Uni Uni Reaction with Competitive Partial Inhibition ni, Uni Uni Reaction with Mixed Complete Inhibition ni, Uni Uni Reaction with Mixed Partial Inhibition ni, Uni Uni Reaction with Non-Competitive Complete Inhibition ni, Uni Uni Reaction with Non-Competitive Partial Inhibition ni, Uni Uni Reaction with Reversible Complete Inhibition ni, Uni Uni Reaction with Reversible Partial Inhibition ni, Uni Uni Reaction with Uncompetitive Complete Inhibition ni, Uni Uni Reaction with Uncompetitive Partial Inhibition ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Task c

Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Task

specific task associated with a mathematical model
has sub-classes
Computational Task c
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Object Properties

applied byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedBy

element applied by another element of the same/another class
has sub-properties
applied by task op
is inverse of
applies op

applied by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedByTask

A mathematical model is applied (used) by a computational task.
has super-properties
applied by op
has domain
Mathematical Model c
has range
Computational Task c
is inverse of
applies model op

appliesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#applies

element applies another element of the same/another class
has sub-properties
applies model op
is inverse of
applied by op

applies modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliesModel

A computational task applies (uses) a mathematical model.
has super-properties
applies op
has domain
Computational Task c
has range
Mathematical Model c
is inverse of
applied by task op

approximated byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedBy

item approximated by another item of the same class

has characteristics: transitive

has sub-properties
approximated by formulation op, approximated by model op, approximated by quantity op, approximated by task op
is inverse of
approximates op

approximated by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByFormulation

A mathematical formulation (e.g. equation) is approximated by another mathematical formulation.

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximates formulation op

approximated by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByModel

A mathematical model is approximated by another mathematical model.

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximates model op

approximated by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByQuantity

A (physical or other) quantity is approximated by another quantity.

has characteristics: transitive

has super-properties
approximated by op
has domain
Quantity c
has range
Quantity c
is inverse of
approximates quantity op

approximated by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByTask

A computational task is approximated by another computational task.

has characteristics: transitive

has super-properties
approximated by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximates task op

approximatesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximates

item approximates another item of the same class

has characteristics: transitive

has sub-properties
approximates formulation op, approximates model op, approximates quantity op, approximates task op
is inverse of
approximated by op

approximates formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesFormulation

A mathematical formulation (e.g. equation) approximates another mathematical formulation.

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximated by formulation op

approximates modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesModel

A mathematical model approximates another mathematical model.

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximated by model op

approximates quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesQuantity

A (physical or other) quantity approximates another quantity.

has characteristics: transitive

has super-properties
approximates op
has domain
Quantity c
has range
Quantity c
is inverse of
approximated by quantity op

approximates taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesTask

A computational task approximates another computational task.

has characteristics: transitive

has super-properties
approximates op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximated by task op

contained as assumption inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsAssumptionIn

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains assumption op

contained as boundary condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsBoundaryConditionIn

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains boundary condition op

contained as constant inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstantIn

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c or Mathematical Formulation c
is inverse of
contains constant op

contained as constraint condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstraintConditionIn

Solutions to a computational task or a mathematical formulation or a mathematical model are subject to a constraint which is expressed as a mathematical formulation, i.e., an equation or an inequality.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains constraint condition op

contained as coupling condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsCouplingConditionIn

Mathematical formulation, i.e., typically an equation, serving to model the interaction of two or more (sub-)systems that are interacting with each other.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains coupling condition op

contained as final condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFinalConditionIn

Similar to initial conditions, but referring to the system state at final time.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains final condition op

contained as formulation inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFormulationIn

Use this property to denote that a mathematical formulation, e.g. an equation, is contained in a (single or coupled) model or formulation or task, e.g., a Darcy equation is contained in a Darcy-Stokes model or formulation or a related task.

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains formulation op

contained as initial condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInitialConditionIn

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,  is a value of an evolving variable at some point in time designated as the initial time.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains initial condition op

contained as input inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInputIn

(base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains input op

contained as objective inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsObjectiveIn

This property serves to indicate that a certain quantity is to be minimized or maximized in a mathematical optimization task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains objective op

contained as output inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsOutputIn

(base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains output op

contained as parameter inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsParameterIn

has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains parameter op

contained in fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInField

A research problem is contained in a research field.
has super-properties
contained in op
has domain
Research Problem c
has range
Research Field c
is inverse of
contains problem op

contained in formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInFormulation

Use this property to denote that a quantity is contained in a formulation e.g. masses are contained in a Newton Equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
contains quantity op

contained in modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInModel

Use this property to denote that a single model is included in a coupled model, e.g. a Darcy model and a Stokes model are included in a Darcy Stokes model.

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contains model op

contained in taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInTask

This indicates that a computational sub-task is contained in a composite task.

has characteristics: transitive

has super-properties
contained in op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contains task op

containsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#contains

item contains another item of the same/another class
has sub-properties
contains assumption op, contains boundary condition op, contains constant op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains input op, contains model op, contains objective op, contains output op, contains parameter op, contains problem op, contains quantity op, contains task op
is inverse of
contained in op

contains assumptionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsAssumption

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as assumption in op

contains boundary conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsBoundaryCondition

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as boundary condition in op

contains constantop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstant

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained as constant in op

contains constraint conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstraintCondition

Solutions to a computational task or a mathematical formulation or a mathematical model are subject to a constraint which is expressed as a mathematical formulation, i.e., an equation or an inequality.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as constraint condition in op

contains coupling conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsCouplingCondition

Mathematical formulation, i.e., typically an equation, serving to model the interaction of two or more (sub-)systems that are interacting with each other.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as coupling condition in op

contains final conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFinalCondition

Similar to initial conditions, but referring to the system state at final time.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as final condition in op

contains formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFormulation

Use this property to denote that a (single or coupled) model or formulation includes a mathematical formulation, e.g. a Darcy Stokes model includes a Darcy equation and a Stokes equation.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as formulation in op

contains initial conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInitialCondition

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,  is a value of an evolving variable at some point in time designated as the initial time.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as initial condition in op

contains inputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInput

Indicates that a (base) quantity is considered as input in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as input in op

contains modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsModel

Use this property to denote that a coupled model includes single models, e.g. a Darcy Stokes model includes a Darcy model and a Stokes model.

has characteristics: transitive

has super-properties
contains op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contained in model op

contains objectiveop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsObjective

This property serves to indicate that a certain quantity is to be minimized or maximized in a computational optimization task. An objective function, a target function, a loss function or cost function (minimization), a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as objective in op

contains outputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsOutput

Indicates that a (base) quantity is considered as output in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as output in op

contains parameterop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsParameter

Auxiliary variable or arbitrary constant that characterizes a system or specifies a mathematical function among a family of functions. This property serves to indicate that a certain quantity is considered as a parameter in a computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as parameter in op

contains problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsProblem

A research field contains a research problem.
has super-properties
contains op
has domain
Research Field c
has range
Research Problem c
is inverse of
contained in field op

contains quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsQuantity

Use this property to denote that a mathematical formulation contains a quantity, e.g., a Newton Equation contains masses.
has super-properties
contains op
has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained in formulation op

contains taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsTask

This indicates that a composite computational task contains a subtask.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contained in task op

defined byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definedBy

A quantity is defined by a mathematical formulation, i.e., an equation.
has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
defines op

definesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#defines

A mathematical formulation, i.e., an equation, serves to define a quantity.
has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
defined by op

discretized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedBy

process of obtaining discrete models/formulations that are the analogues of continuous models/formulations
has sub-properties
discretized by formulation op, discretized by model op, discretized by task op
is inverse of
discretizes op

discretized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
has super-properties
discretized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretizes formulation op

discretized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Note that certain models are already discretized from the outset.
has super-properties
discretized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretizes model op

discretized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByTask

task discretized by another task
has super-properties
discretized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretizes task op

discretizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizes

process of obtaining discrete models/formulations that are the analogues of continuous models/formulations
has sub-properties
discretizes formulation op, discretizes model op, discretizes task op
is inverse of
discretized by op

discretizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
has super-properties
discretizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretized by formulation op

discretizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models, thus making them computer representable and hopefully(!) computer solvable. Note that certain models are already discretized from the outset.
has super-properties
discretizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretized by model op

discretizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesTask

task discretizes another task
has super-properties
discretizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretized by task op

documented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documentedIn

property to express that an entity (problem, model, ...) is documented in a specific publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
documents op

documentsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documents

property that expresses that a publication is documenting some entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
documented in op

generalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedBy

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has sub-properties
generalized by field op, generalized by formulation op, generalized by model op, generalized by problem op, generalized by quantity op, generalized by task op
is inverse of
generalizes op

generalized by fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByField

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Field c
has range
Research Field c
is inverse of
generalizes field op

generalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByFormulation

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalizes formulation op

generalized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByModel

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalizes model op

generalized by problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByProblem

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalizes problem op

generalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByQuantity

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Quantity c
has range
Quantity c or Quantity Kind c
is inverse of
generalizes quantity op

generalized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByTask

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalizes task op

generalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizes

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has sub-properties
generalizes field op, generalizes formulation op, generalizes model op, generalizes problem op, generalizes quantity op, generalizes task op
is inverse of
generalized by op

generalizes fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesField

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Field c
has range
Research Field c
is inverse of
generalized by field op

generalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesFormulation

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalized by formulation op

generalizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesModel

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalized by model op

generalizes problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesProblem

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalized by problem op

generalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesQuantity

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c
is inverse of
generalized by quantity op

generalizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesTask

Form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

has characteristics: transitive

has super-properties
generalizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalized by task op

invented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inventedIn

property that states that some entity (problem, model, ...) was invented in a specific publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
invents op

inventsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#invents

property that states that a publication invented some entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
invented in op

linearized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedBy

property that states that a formulation is linearized (exact or approximate) by another formulation
has sub-properties
linearized by formulation op, linearized by model op, linearized by quantity op, linearized by task op
is inverse of
linearizes op

linearized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByFormulation

A property that states that a formulation is linearized (exact or approximate) by another formulation.
has super-properties
linearized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearizes formulation op

linearized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByModel

A property that states that a model is linearized (exact or approximate) by another model.
has super-properties
linearized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearizes model op

linearized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByQuantity

A property that states that a quantity is linearized (exact or approximate) by another quantity.
has super-properties
linearized by op
has domain
Quantity c
has range
Quantity c
is inverse of
linearizes quantity op

linearized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByTask

A property that states that a task is linearized (exact or approximate) by another task.
has super-properties
linearized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearizes task op

linearizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizes

linearization of a formulation, model, quantity or task
has sub-properties
linearizes formulation op, linearizes model op, linearizes quantity op, linearizes task op
is inverse of
linearized by op

linearizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesFormulation

A property that states that a formulation linearizes (exact or approximate) another formulation.
has super-properties
linearizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearized by formulation op

linearizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesModel

A property that states that a model linearizes (exact or approximate) another model.
has super-properties
linearizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearized by model op

linearizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesQuantity

A property that states that a quantity linearizes (exact or approximate) another quantity.
has super-properties
linearizes op
has domain
Quantity c
has range
Quantity c
is inverse of
linearized by quantity op

linearizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesTask

A property that states that a task linearizes (exact or approximate) another task.
has super-properties
linearizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearized by task op

modeled byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#modeledBy

mathematical modeling of a part of the reality
has domain
Research Problem c
has range
Mathematical Model c
is inverse of
models op

modelsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#models

mathematical modeling of a part of the reality
has domain
Mathematical Model c
has range
Research Problem c
is inverse of
modeled by op

nondimensionalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedBy

partial or full removal of physical dimensions from a quantity or a formulation

has characteristics: inverse functional

has sub-properties
nondimensionalized by formulation op, nondimensionalized by quantity op
is inverse of
nondimensionalizes op

nondimensionalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByFormulation

A property that states that a formulation is nondimensionalized (partially or completely) by another formulation.
has super-properties
nondimensionalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalizes formulation op

nondimensionalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByQuantity

A property that states that a quantity is nondimensionalized (partially or completely) by another quantity.
has super-properties
nondimensionalized by op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalizes quantity op

nondimensionalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizes

partial or full removal of physical dimensions from a quantity or a formulation

has characteristics: functional

has sub-properties
nondimensionalizes formulation op, nondimensionalizes quantity op
is inverse of
nondimensionalized by op

nondimensionalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizesFormulation

A property that states that a formulation nondimensionalizes (partially or completely) another formulation.
has super-properties
nondimensionalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalized by formulation op

nondimensionalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionaliesQuantity

A property that states that a quantity nondimensionalizes (partially or completely) another quantity.
has super-properties
nondimensionalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalized by quantity op

similar toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarTo

property describing that two entities are similar

has characteristics: symmetric, transitive

has sub-properties
similar to field op, similar to formulation op, similar to model op, similar to problem op, similar to quantity op, similar to task op

similar to fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToField

Use this property only if the two research fields are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Field c
has range
Research Field c

similar to formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToFormulation

Use this property only if the two mathematical formulations are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c

similar to modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToModel

Use this property only if the two mathematical models are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Model c
has range
Mathematical Model c

similar to problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToProblem

Use this property only if the two research problems are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Problem c
has range
Research Problem c

similar to quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToQuantity

Use this property only if the two quantities are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c

similar to taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToTask

Use this property only if the two computational tasks are similar but the one is not the generalization of the other one.

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Computational Task c
has range
Computational Task c

studied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studiedIn

This property states that an entity (problem, model, ...) is studied in a specific Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
studies op

studiesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studies

This property states that a Publication studies an entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
studied in op

surveyed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveyedIn

This property states that an entity (problem, model, application, ...) is surveyed in a specific Publication. Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
surveys op

surveysop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveys

This property states that a Publication surveys some entity (problem, model, application...). Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
surveyed in op

used inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#usedIn

A property that states that an entity (problem, model, ...) is used in a Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
uses op

usesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#uses

A property that states that a Publication uses a specific entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
used in op

Data Properties

defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definingFormulation

can be equations, inequalities, expressions, logic quantifiers or other
has super-properties
formulation property dp
has domain
Mathematical Formulation c
has range
La Te X ep or Math M L ep

formulation propertydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#formulationProperty

properties dealing with mathematical formulations
has sub-properties
defining formulation dp, in defining formulation dp
has domain
Mathematical Formulation c

in defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inDefiningFormulation

symbol or term of formulation and corresponding quantity
has super-properties
formulation property dp
has domain
Mathematical Formulation c
has range
string or La Te X ep or Math M L ep

is convexdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isConvex

true if convex, false if concave
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is deterministicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDeterministic

true, if the model is deterministic; false, if the model is probabilistic (stochastic)
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is dimensionlessdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDimensionless

true, if physical dimensions are partially or fully removed
has domain
Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c
has range
boolean

is dynamicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDynamic

True, if dynamic; false, if static
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is lineardp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isLinear

True, if linear; false, if non-linear
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
boolean

is space-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isSpaceContinuous

has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is time-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isTimeContinuous

True, if continuous in time; false, if discrete in time
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

Annotation Properties

abstractap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/abstract

alt Labelap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#altLabel

arxiv I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#arxivID

bibliographic Citationap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/bibliographicCitation

broaderap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#broader

close Matchap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#closeMatch

contributorap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/contributor

createdap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/created

creatorap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/creator

dbpedia I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#dbpediaID

definitionap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2000/01/rdf-schema#definition

descriptionap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/description

doi I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#doiID

is Replaced Byap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/isReplacedBy

issuedap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/issued

licenseap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/license

mardi I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#mardiID

modifiedap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/modified

publisherap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/publisher

qudt I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#qudtID

referencesap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/references

rightsap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/rights

subjectap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/subject

titleap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/title

was Derived Fromap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/ns/prov#wasDerivedFrom

wikidata I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#wikidataID

zbmath I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#zbmathID

Named Individuals

Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Acceleration

rate at which the magnitude and/or direction of velocity changes with time
belongs to
Quantity Kind c
has facts
qudt I D ap Acceleration ep
wikidata I D ap Q11376 ep

Action Potential Propagation Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Action_Potential_Propagation_Model

propagation of the action potential
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Accounts for the propagation of the action potential. Necessary because Subcellular model only considers isolated processes in one sacomere"@en
doi I D ap gamm.202370009 ep

Active Contractile Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ActiveContractileForce

active force generated by the contractile element
belongs to
Quantity c
has facts
defined by op Active Contractile Force (Definition) ni

Active Contractile Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ActiveContractileForceDefinition

active force generated by the contractile element
belongs to
Mathematical Formulation c
has facts
contains quantity op Active Contractile Force ni
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Muscle Contraction Velocity ni
contains quantity op Muscle Length ni
contains quantity op Time ni
defining formulation dp "$F_{\text{ACE}}(t) \equiv F^{\text{M}}_{0} \cdot a(t) \cdot f_{\text{L}}(\mathcal{l}_{\text{M}}(t)) \cdot f_{\text{v}} (\nu_{\text{M}}(t))$"^^La Te X ep
in defining formulation dp "$F^{\text{M}}_{0}$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{ACE}}$, Active Contractile Force"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{M}}$, Muscle Length"^^La Te X ep
in defining formulation dp "$\nu_{\text{M}}$, Muscle Contraction Velocity"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Adjacency Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AdjacencyMatrix

square matrix used to represent a graph or network
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q727035 ep

Age Of An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AgeOfAnIndividual

time elapsed since an individual was born
belongs to
Quantity c
has facts
generalized by quantity op Time ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q185836 ep

Allee Effectni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AlleeEffect

effect to model the infection rate as a function of population density
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Population Density ni
defining formulation dp "$1 - \dfrac{A}{n + n_0} \geq \frac{1}{3}$"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
description ap "The Allee effect is used to model the infection rate as a function of population density, where it represents a lower transmission probability in less densely populated regions. We adopt the effect and bound it from below by 1/3. This ensures that the effect is at most three times lower in sparsely populated areas than in regions with high population density. To enforce the lower bound, we apply a shift n0 in the Allee term. We choose $n_0 = \frac{3}{2}A$"@en
wikidata I D ap Q2301505 ep

Allee Thresholdni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AlleeThreshold

population density below which growth becomes negative
belongs to
Quantity c

Ampere Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AmpereLaw

Ampère's circuital law (with Maxwell's addition) relates the integrated magnetic field around a closed loop to the electric current passing through the loop
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Current Density ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Permeability (Vacuum) ni
contains quantity op Permittivity (Vacuum) ni
contains quantity op Time ni
defining formulation dp "$\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$E$, Magnetic Field"^^La Te X ep
in defining formulation dp "$J$, Electric Current Density"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\mu_0$, Permeability (Vacuum)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
wikidata I D ap Q51500 ep

Amplitude Of Electron Waveni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AmplitudeOfElectronWave

amplitude of the wave function representing an electron
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni

Angular Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AngularMomentum

measure of the extent to which an object will continue to rotate in the absence of an applied torque
belongs to
Quantity Kind c
has facts
generalizes quantity op Planck Constant ni
qudt I D ap Angular Momentum ep
wikidata I D ap Q161254 ep

Anharmonicity Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AnharmonicityConstant

deviation of a physical system from being a harmonic oscillator
belongs to
Quantity c
has facts
defined by op Anharmonicity Constant (Definition) ni
wikidata I D ap Q545228 ep

Anharmonicity Constant (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AnharmonicityConstantDefinition

deviation of a physical system from being a harmonic oscillator
belongs to
Mathematical Formulation c
has facts
contains quantity op Anharmonicity Constant ni
contains quantity op Coriolis Coupling Constant ni
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Number of Particles ni
contains quantity op Rotational Constant ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$ \begin{align} \chi_{rr} &=& \frac{1}{16} \phi_{rrrr} - \frac{1}{16} \sum_{s=1}^{3N-6} \phi_{rrs}^2 \frac {8\omega_r^2-3\omega_s^2} {\omega_s(4\omega_r^2-\omega_s^2)} \\ \chi_{rs} &=&\frac{1}{4} \phi_{rrss} - \frac{1}{4} \sum_{t=1}^{3N-6} \frac{\phi_{rrt}\phi_{tss}}{\omega_t} - \frac{1}{2} \sum_{t=1}^{3N-6} \frac {\phi_{rst}^2 \omega_t (\omega_t^2-\omega_r^2-\omega_s^2)} {\Delta_{rst}} \\ &+& \left[ A(\zeta_{r,s}^{(a)})^2 + B(\zeta_{r,s}^{(b)})^2 + C(\zeta_{r,s}^{(c)})^2 \right] \left[ \frac{\omega_r}{\omega_s} + \frac{\omega_s}{\omega_r} \right] \\ \Delta_{rst} &=& ( \omega_r + \omega_s + \omega_t ) ( \omega_r - \omega_s - \omega_t ) (-\omega_r + \omega_s - \omega_t ) (-\omega_r - \omega_s + \omega_t ) \end{align}$"^^La Te X ep
in defining formulation dp "$A,B,C$, Rotational Constant"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\chi$, Anharmonicity Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibrational Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$\zeta$, Coriolis Coupling Constant"^^La Te X ep
description ap "Derived by using second order (non-degenerate) perturbation theory, considering the comparable magnitude of contributions of cubic anharmonicity in second order and quartic anharmonicity in first order."@en
wikidata I D ap Q545228 ep

Applied External Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AppliedExternalVoltage

external voltage at an Ohmic contact in semiconductor physics|technology
belongs to
Quantity c
has facts
contained in formulation op Dirichlet Boundary Condition For Electric Potential ni
generalized by quantity op Voltage ni

Archaeologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Archaeology

study of the past via material culture
belongs to
Research Field c
has facts
generalizes field op Egyptology ni
mardi I D ap Item: Q65133 ep
wikidata I D ap Q23498 ep

Areani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Area

quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane
belongs to
Quantity Kind c
has facts
wikidata I D ap Q11500 ep

Artificial Neural Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Artificial_Neural_Network

computational model used in machine learning, based on connected, hierarchical functions
belongs to
Mathematical Model c
has facts
generalizes model op Recurrent Neural Network ni
wikidata I D ap Q192776 ep

Astronomyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Astronomy

scientific study of celestial objects and phenomena
belongs to
Research Field c
has facts
mardi I D ap Item: Q71225 ep
wikidata I D ap Q333 ep

Asymptomatic Infection Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AsymptomaticInfectionRate

constant representing the asymptomatic infection rate
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Asymptomatic Recovery Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AsymptomaticRecoveryRate

constant representing the asymptomatic recovery rate
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Attraction Force At Opinionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AttractionForceAtOpinion

attraction force at an individuals opinion by influencers and media
belongs to
Quantity c

Attraction Force At Opinion Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AttractionForceAtOpinionFormulation

attraction force at a specific opinion x
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Attraction Force At Opinion ni
contains quantity op Opinion ni
contains quantity op Overall Distribution Of Individuals ni
contains quantity op Pair Function ni
contains quantity op Parameter To Scale Attractive Force From Influencers ni
contains quantity op Parameter To Scale Attractive Force From Media ni
contains quantity op Parameter To Scale Attractive Force From Other Individuals ni
defining formulation dp "$\mathcal{F}(x, y_m, z_l, \rho) = a \frac{\int_D \rho(x', t) \varphi(\|x' - x\|)(x' - x) \, dx'}{\int_D \rho(x', t) \varphi(\|x' - x\|) \, dx'} + b (y_m(t) - x) + c (z_l(t) - x)$"^^La Te X ep
in defining formulation dp "$\mathcal{F}$, Attraction Force At Opinion"^^La Te X ep
in defining formulation dp "$\phi$, Pair Function"^^La Te X ep
in defining formulation dp "$\rho$, Overall Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$a$, Parameter To Scale Attractive Force From Other Individuals"^^La Te X ep
in defining formulation dp "$b$, Parameter To Scale Attractive Force From Media"^^La Te X ep
in defining formulation dp "$c$, Parameter To Scale Attractive Force From Influencers"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Average Opinion Of Followers Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfInfluencerFollowers

opinion of the influencers is drawn towards the average opinion of the followers
belongs to
Quantity c

Average Opinion Of Followers Of Influencers In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersInThePartialFieldModel

opinion of the influencers is drawn towards the average opinion of the followers
belongs to
Quantity c

Average Opinion Of Followers Of Infuencers Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersFormulation

equation describing the average opinon of the followers of a specific Influencer
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Influencers ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Time ni
defining formulation dp "$\hat{x}_l(t)=\frac{1}{\sum_k C_{k l}(t)} \sum_{i=1}^N C_{i l}(t) x_i(t)$"^^La Te X ep
in defining formulation dp "$C_l(t)$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x_i(t)$, Opinion Vector of Individuals"^^La Te X ep
is space-continuous dp "true"^^boolean

Average Opinion Of Followers Of Infuencers In The Partial Mean Field Model Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersInThePartialFieldModelFormulation

equation describing the average opinon of the followers of a specific influencer in the partial mean field opinion model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Medium Influencer Fraction Limit ni
contains quantity op Opinion ni
contains quantity op Time ni
defining formulation dp "$\hat{x}_l(t)=\frac{\sum_{m=1}^M \int_D x \rho_{m, l}(x, t) d x}{\sum_{m=1}^M n_{m, l}(t)}$"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Influencers In The Partial Field Model"^^La Te X ep
in defining formulation dp "$\rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$n_{m,l}$, Medium Influencer Fraction Limit"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Average Opinion Of Followers Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfMediaFollowers

opinion of the media is drawn towards the average opinion of the followers of that medium
belongs to
Quantity c

Average Opinion Of Followers Of Media Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaFormulation

equation describing the average opinon of the followers of a specific medium
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Media ni
contains quantity op Medium Follower Matrix ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Time ni
defining formulation dp "$\tilde{x}_m(t)=\frac{1}{\sum_k B_{k m}(t)} \sum_{i=1}^N B_{i m}(t) x_i(t) $"^^La Te X ep
in defining formulation dp "$B_m(t)$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x_i(t)$, Opinion Vector of Individuals"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean

Average Opinion Of Followers Of Media In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaInThePartialFieldModel

opinion of the media is drawn towards the average opinion of the followers of that medium
belongs to
Quantity c

Average Opinion Of Followers Of Media In The Partial Mean Field Model Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaInThePartialFieldModelFormulation

equation describing the average opinon of the followers of a specific medium in the partial field opinion model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Media In The Partial Mean Field Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Medium Influencer Fraction Limit ni
contains quantity op Opinion ni
contains quantity op Time ni
defining formulation dp "$\tilde{x}_m(t)=\frac{\sum_{l=1}^L \int_D x \rho_{m, l}(x, t) d x}{\sum_{l=1}^L n_{m, l}(t)}$"^^La Te X ep
in defining formulation dp "$\rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media In The Partial Field Model"^^La Te X ep
in defining formulation dp "$n_{m,l}$, Medium Influencer Fraction Limit"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Azimuthal Angleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AzimuthalAngle

angle in the spherical coordinate system
belongs to
Quantity Kind c
has facts
wikidata I D ap Q116757767 ep

Balanced Truncationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancedTruncation

powerful technique to reduce the state-space dimension of a dynamical system
belongs to
Computational Task c
has facts
applies model op Control System Model ni
contains formulation op Balancing Transformation ni
contains formulation op Lyapunov Equation ni
generalizes task op Balanced Truncation (Linear) ni
description ap "The basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace, hopefully without changing the overall response of the system too much."@en
description ap "This approach is based on balancing the controllable and observable subspaces, and exploits the properties of the underlying dynamical system in that it uses the properties of the controllability and observability Gramians to identify suitable small parameters that are sent to 0 to yield a reduced-order system"@en
doi I D ap 3 540 27909 1 3 ep
doi I D ap 1.3605243 ep
doi I D ap jcd.2020001 ep

Balanced Truncation (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancedTruncationLinear

powerful technique to reduce the state-space dimension of a dynamical system with linear input equation
belongs to
Computational Task c
has facts
applies model op Control System Model (Linear) ni
contains formulation op Balancing Transformation ni
contains formulation op Control System Input Linear ni
contains formulation op Control System Input Linear (Reduced) ni
contains formulation op Control System Output Linear ni
contains formulation op Control System Output Linear (Reduced) ni
contains formulation op Lyapunov Equation Controllability ni
contains formulation op Lyapunov Equation Observability ni
contains initial condition op Initial Control State ni
contains input op Control System Matrix A ni
contains input op Control System Matrix B ni
contains input op Control System Matrix C ni
contains output op Control System Matrix A (Reduced) ni
contains output op Control System Matrix B (Reduced) ni
contains output op Control System Matrix C (Reduced) ni
contains output op MOR Transformation Matrix ni
description ap "In the case of a linear control system, a useful property of balanced truncation is that it admits easy control of the approximation error when truncating states."@en

Balancing Transformationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancingTransformation

coordinate transformation T under which controllability and observability Gramians become equal and diagonal matrices comprising the Hankel singular values
belongs to
Mathematical Formulation c
has facts
contains quantity op Gramian Matrix Controllability ni
contains quantity op Gramian Matrix Observability ni
contains quantity op Hankel Singular Value ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$T^{-1}W_c\left(T^{-1}\right)^{*} = T^{*}W_oT = \left( \begin{array}{lll} \sigma_{1} & & 0 \\ & \ddots & \\ 0 & & \sigma_{n} \end{array}\right) = \Sigma$"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep
in defining formulation dp "$\sigma$, Hankel Singular Value"^^La Te X ep
description ap "The transformation T is a contragredient transformation and exists whenever $W_c$, $W_o$ are symmetric and positive definite. Note that the squared HSVs are the eigenvalues of the product of $W_c$ and $W_o$."@en

Band Edge Energy For Conduction Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BandEdgeEnergyForConductionBand

energy of the lower edge of the electronic conduction band
belongs to
Quantity c
has facts
generalized by quantity op Energy ni

Band Edge Energy For Valence Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BandEdgeEnergyForValenceBand

energy of the upper edge of the electronic valence band
belongs to
Quantity c
has facts
generalized by quantity op Energy ni

Beavers-Joseph Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BeaversJosephCoefficient

coefficient for the coupling of a Stokes model and a Darcy model
belongs to
Quantity c

Beavers–Joseph-Saffman Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BeaversJosephSaffmanCondition

boundary condition between an unconfined incompressible viscous fluid (Stokes model) and fluid inside a porous medium (Darcy model)
belongs to
Mathematical Formulation c
has facts
contains quantity op Beavers-Joseph Coefficient ni
contains quantity op Fluid Dynamic Viscosity (Free Flow) ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Fluid Viscous Stress ni
contains quantity op Unit Normal Vector ni
contains quantity op Unit Tangent Vector ni
defining formulation dp "$[(v + \sqrt{K}(\alpha_{\mathrm{BJ}}\mu)^{-1} \tau n)\cdot t_{\mathrm{ff,pm}}]^{ff} = 0 \quad \mathrm {on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$K$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\alpha_{BJ}$, Beavers-Joseph Coefficient"^^La Te X ep
in defining formulation dp "$\mu$, Fluid Dynamic Viscosity (Free Flow)"^^La Te X ep
in defining formulation dp "$\tau$, Fluid Viscous Stress"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$t_{\mathrm{ff,pm}}$, Tangent Unit Vector"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
doi I D ap s11242 009 9344 y ep
doi I D ap S0022112067001375 ep

Between Population Contact Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BetweenPopulationContactRate

contact rate of one sub-population with all other sub-populations
belongs to
Quantity c
has facts
generalized by op Rate ni
is dimensionless dp "false"^^boolean
description ap "Used in multi-population models."@en

Between Population Contact Rate Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BetweenPopulationContactRateEquation

contact rate of one sub-population with all other subpopulations
belongs to
Mathematical Formulation c
has facts
contains quantity op Between Population Contact Rate ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defines op Between Population Contact Rate ni
defining formulation dp "$a_i = \sum_{k\neq i}\alpha_{ik} \Delta t N^k/N^i$"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Bi Bi Reaction following Theorell-Chance Mechanismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionfollowingTheorellChanceMechanism

bi bi reaction with a Theorell-Chance mechanism
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Bi Bi Reaction Ordered Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismODEModel

bi bi reaction model following an ordered mechanism
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ordered Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
models op Bi Bi Reaction following Ordered Mechanism ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - substrate 1 - substrate 2 - complex, enzyme - product 1 - product 2 - complex, enzyme - product 1 complex and product 1 and 2 in a Bi Bi Reaction following the Ordered Mechanism. k_{i} with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step."@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct1SS

bi bi reaction Michaelis Menten model following an ordered mechanism with product 1 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct1ansSingleCCSS

bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with product 1 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct2SS

bi bi reaction Michaelis Menten model following an ordered mechanism with product 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct2ansSingleCCSS

bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with product 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProducts1and2SS

bi bi reaction Michaelis Menten model following an ordered mechanism with products 1 and 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProducts1and2ansSingleCCSS

bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with products 1 and 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithoutProductsSS

bi bi reaction Michaelis Menten model following an ordered mechanism without products formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithoutProductsansSingleCCSS

bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism without products formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ordered Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechansimODESystem

system of ordinary differential equations describing a bi bi reaction with an ordered mechanism
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ordered) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 1 Complex Concentration ni
contains quantity op Enzyme - Product 1 - Product 2 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 - Substrate 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Product 1 Complex ni
contains quantity op Reaction Rate of Enzyme - Product 1 - Product 2 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} c_{ES_{1}S_{2}} - k_{2} c_{ES_1} c_{S_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} c_{E} c_{S_1} + k_{-2} c_{ES_{1}S_{2}} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2} \\ \frac{dc_{ES_{1}S_{2}}}{dt} &= k_{2} c_{ES_1} c_{S_2} + k_{-3} c_{EP_{1}P_{2}} - k_{-2} c_{ES_{1}S_{2}} - k_{3} c_{ES_{1}S_{2}} \\ \frac{dc_{EP_{1}P_{2}}}{dt} &= k_{3} c_{ES_{1}S_{2}} + k_{-4} c_{EP_1} c_{P_2} - k_{-3} c_{EP_{1}P_{2}} - k_{4} c_{EP_{1}P_{2}} \\ \frac{dc_{EP_1}}{dt} &= k_{4} c_{EP_{1}P_{2}} + k_{-5} c_{E} c_{P_1} - k_{-4} c_{EP_1} c_{P_2} - k_{5} c_{EP_1} \\ \frac{dc_{P_1}}{dt} &= k_{5} c_{EP_1} - k_{-5} c_{E} c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} c_{EP_{1}P_{2}} - k_{-4} c_{EP_1} c_{P_2} \\ \frac{dc_{E}}{dt} &= k_{-1} c_{ES_1} + k_5 c_{EP_1} - k_{1} c_{E} c_{S_1} - k_{-5} c_{E} c_{P_1} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1P_2}}{dt}$, Reaction Rate of Enzyme - Product 1 - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1}}{dt}$, Reaction Rate of Enzyme - Product 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1S_2}}{dt}$, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_1P_2}$, Enzyme - Product 1 - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Enzyme - Product 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1S_2}$, Enzyme - Substrate 1 - Substrate 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Ordered Mechanism with single central Complex (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismODEModelsingleCC

bi bi reaction with single central complex model following an ordered mechanism
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ordered Mechanism with single central Complex ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
models op Bi Bi Reaction following Ordered Mechanism with single central complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - substrate 1 - substrate 2 = enzyme - product 1 - product 2 - complex, enzyme - product 1 - complex and product 1 and 2 in a Bi Bi Reaction following the Ordered Mechanism with a single central Complex. k_{i} with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step."@en

Bi Bi Reaction Ordered Mechanism with single central Complex ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechansimODESystemsingleCC

system of ordinary differential equations describing a bi bi reaction with an ordered mechanism and single central complex
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{2} c_{ES_1} c_{S_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} c_{E} c_{S_1} + k_{-2} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2} \\ \frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt} &= k_{2} c_{ES_1} c_{S_2} - k_{-2} c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-4} c_{EP_1} c_{P_2} - k_{4} c_{ES_{1}S_{2}=EP_{1}P_{2}} \\ \frac{dc_{EP_1}}{dt} &= k_{4} c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-5} c_{E} c_{P_1} - k_{-4} c_{EP_1} c_{P_2} - k_{5} c_{EP_1} \\ \frac{dc_{P_1}}{dt} &= k_{5} c_{EP_1} - k_{-5} c_{E} c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-4} c_{EP_1} c_{P_2} \\ \frac{dc_{E}}{dt} &= k_{-1} c_{ES_1} + k_5 c_{EP_1} - k_{1} c_{E} c_{S_1} - k_{-5} c_{E} c_{P_1} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1}}{dt}$, Reaction Rate of Enzyme - Product 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt}$, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Enzyme - Product 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Ping Pong Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechansimODEModel

bi bi reaction model following a ping-pong mechanism
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ping Pong Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
models op Bi Bi Reaction following Ping Pong Mechanism ni
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, intermediate, intermediate - substrate 2 - complex, product 1 and 2) in a Bi Bi Reaction following the Ping Pong Mechanism. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step."@en

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProduct1SS

bi bi reaction Michaelis Menten model following a ping-pong mechanism with product 1 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni
similar to model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProduct2SS

bi bi reaction Michaelis Menten model following a ping-pong mechanism with product 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni
similar to model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProducts1and2SS

bi bi reaction Michaelis Menten model following a ping-pong mechanism with products 1 and 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithoutProductsSS

bi bi reaction Michaelis Menten model following a ping-pong mechanism without products formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Ping Pong Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechansimODESystem

system of ordinary differential equations describing a bi bi reaction with a ping pong mechanism
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Intermediate Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Intermediate Concentration ni
contains quantity op Intermediate - Substrate 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Intermediate ni
contains quantity op Reaction Rate of Intermediate - Substrate 2 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-3} c_{E*S_2} - k_{3} c_{E*} c_{S_2} \\ \frac{dc_{E}}{dt} &= k_{-1} c_{ES_1} + k_{4} c_{E*S_2} - k_{1} c_{E} c_{S_1} - k_{-4} c_{E} c_{P_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} c_{E} c_{S_1} + k_{-2} c_{E*} c_{P_1} - k_{-1} c_{ES_1} - k_{2} c_{ES_1} \\ \frac{dc_{E*}}{dt} &= k_{2} c_{ES_1} + k_{-3} c_{E*S_2} - k_{-2} c_{E*} c_{P_1} - k_{3} c_{E*} c_{S_2} \\ \frac{dc_{E*S_2}}{dt} &= k_{3} c_{E*} c_{S_2} + k_{-4} c_{E} c_{P_2} - k_{-3} c_{E*S_2} - k_{4} c_{E*S_2} \\ \frac{dc_{P_1}}{dt} &= k_{2} c_{ES_1} - k_{-2} c_{E*} c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} c_{E*S_2} - k_{-4} c_{P_2} c_{E} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*S_2}}{dt}$, Reaction Rate of Intermediate - Substrate 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*}}{dt}$, Reaction Rate of Intermediate"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Intermediate - Substrate 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Intermediate Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Theorell-Chance Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechansimODEModel

bi bi reaction model following a Theorell-Chance mechanism
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Theorell-Chance Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
models op Bi Bi Reaction following Theorell-Chance Mechanism ni
description ap "Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - product 2 - complex, product 1 and 2) in a Bi Bi Reaction following the Theorell-Chance Mechanism. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step."@en

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProduct1SS

bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with product 1 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 ni
similar to model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProduct2SS

bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with product 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProducts1and2SS

bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with products 1 and 2 formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithoutProductsSS

bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism without products formulated via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Bi Bi Reaction Theorell-Chance Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechansimODESystem

system of ordinary differential equations describing a bi bi reaction with a Theorell-Chance mechanism
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 2 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Product 2 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} c_{EP_2} c_{P_1} - k_{2} c_{ES_1} c_{S_2} \\ \frac{dc_{P_1}}{dt} &= k_{2} c_{ES_1} c_{S_2} - k_{-2} c_{EP_2} c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{3} c_{EP_2} - k_{-3} c_{E} c_{P_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} c_{E} c_{S_1} + k_{-2} c_{EP_{2}} c_{P_1} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2} \\ \frac{dc_{EP_2}}{dt} &= k_{2} c_{ES_1} c_{S_2} + k_{-3} c_{E} c_{P_2} - k_{-2} c_{EP_2} c_{P_1} - k_3 c_{EP_2} \\ \frac{dc_{E}}{dt} &= k_{-1} c_{ES_1} + k_3 c_{EP_2} - k_{1} c_{E} c_{S_1} - k_{-3} c_{E} c_{P_2} \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_2}}{dt}$, Reaction Rate of Enzyme - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Enzyme - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Binary Decision Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BinaryDecisionVariable

binary variable deciding if an object is chosen or not
belongs to
Quantity c
has facts
defined by op Binary Decision Variable (Definition) ni
description ap "In case of line pool generation, it decides if a line is included or not"@en

Binary Decision Variable (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BinaryDecisionVariableDefinition

binary variable deciding if an object is chosen or not
belongs to
Mathematical Formulation c
has facts
contains quantity op Binary Decision Variable ni
defining formulation dp "$x_l \equiv \left\{ \begin{array}{ll} 1 & l \textrm{is chosen}\\ o & \textrm{otherwise} \\ \end{array} \right. $"^^La Te X ep
in defining formulation dp "$x_l$, Binary Decision Variable"^^La Te X ep

Biologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biology

scientific study of living things, especially their structure, function, growth, evolution, and distribution
belongs to
Research Field c
has facts
mardi I D ap Item: Q59666 ep
wikidata I D ap Q420 ep

Biomechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biomechanics

study of the structure and function of the mechanical aspects of biological systems
belongs to
Research Field c
has facts
contains problem op Muscle Movement ni
wikidata I D ap Q193378 ep

Biophysicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biophysics

study of biological systems using methods from the physical sciences
belongs to
Research Field c
has facts
generalized by field op Biology ni
generalizes field op Biomechanics ni
wikidata I D ap Q7100 ep

Birth Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BirthRate

total number of live births per 1,000 population divided by the length of a given period in years
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "false"^^boolean
description ap "Birth Rate to be used in the SIR and SIS Models with Births and Deaths. Note that, it is assumed that death rate = birth rate"@en
wikidata I D ap Q203516 ep

Bisswanger (2017) Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Bisswanger_2017_Enzyme_Kinetics

publication
belongs to
Publication c
has facts
surveys op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
doi I D ap 9783527806461 ep

Boltzmann Approximation For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannApproximationForElectrons

Boltzmann approximation for electrons; for use in semiconductor physics
belongs to
Mathematical Formulation c
has facts
contains quantity op Band Edge Energy For Conduction Band ni
contains quantity op Boltzmann Constant ni
contains quantity op Density Of Electrons ni
contains quantity op Density Of States For Conduction Band ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Temperature ni
defining formulation dp "$n(\psi,\phi_n)=N_c\exp\left(\frac{q(\psi-\phi_n)-E_c}{k_BT}\right)$"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"
in defining formulation dp "$E_c$, Band Edge Energy For Conduction Band"^^La Te X ep
in defining formulation dp "$N_c$, Density Of States For Conduction Band"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Boltzmann Approximation For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannApproximationForHoles

Boltzmann approximation for holes; for use in semiconductor physics
belongs to
Mathematical Formulation c
has facts
contains quantity op Band Edge Energy For Valence Band ni
contains quantity op Boltzmann Constant ni
contains quantity op Density Of Holes ni
contains quantity op Density Of States For Valence Band ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Temperature ni
defining formulation dp "$p(\psi,\phi_p)=N_v\exp\left(\frac{q(\phi_p-\psi)+E_v}{k_BT}\right)$"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"
in defining formulation dp "$E_v$, Band Edge Energy For Valence Band"^^La Te X ep
in defining formulation dp "$N_v$, Density Of States For Valence Band"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Boltzmann Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannConstant

physical constant relating the average relative thermal energy with the thermodynamic temperature
belongs to
Quantity c
has facts
qudt I D ap Boltzmann Constant ep
wikidata I D ap Q5962 ep

Boolean Ringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BooleanRing

in mathematics, a ring that consists of only idempotent elements
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q2634401 ep

Boolean Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BooleanVariable

data type that represents true or false values
belongs to
Quantity Kind c
has facts
generalizes quantity op Object Property ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q520777 ep

Boundary Conditions of Electrophysiological Muscle ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Boundary_Conditions_for_Electrophysiological_Muscle_ODE_System

kinematic and dynamic conditions at the interfaces beween each muscle and the tendon
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Electrophysiological Muscle ODE System ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Material Point Displacement ni
contains quantity op Material Point Velocity ni
contains quantity op Stress Tensor (Piola-Kirchhoff) ni
defining formulation dp "$$\begin{array}{cccc} \mathbf{x}_{\text{M}1} = \mathbf{x}_{\text{T}}, &\dot{\mathbf{x}}_{\text{M}1} = \dot{\mathbf{x}}_{\text{T}}, & \mathbf{P}(\mathbf{F}_{\text{M}1})=\mathbf{P}(\mathbf{F}_{\text{T}}), & \text{on $\partial \Omega_{\text{M}1-\text{T}}$} \\ \mathbf{x}_{\text{M}2} = \mathbf{x}_{\text{T}}, &\dot{\mathbf{x}}_{\text{M}2} = \dot{\mathbf{x}}_{\text{T}}, & \mathbf{P}(\mathbf{F}_{\text{M}2})=\mathbf{P}(\mathbf{F}_{\text{T}}), & \text{on $\partial \Omega_{\text{M}2-\text{T}}$} \end{array}$$"^^La Te X ep
in defining formulation dp "$\dot{\mathbf{x}}$, Material Point Velocity"^^La Te X ep
in defining formulation dp "$\mathbf{P}$, Stress Tensor (Piola-Kirchhoff)"^^La Te X ep
in defining formulation dp "$\mathbf{x}$, Material Point Displacement"^^La Te X ep
in defining formulation dp "$x$, Displacement Muscle Tendon"^^La Te X ep

Briggs (1925) A note on the kinetics of enzyme actionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Briggs_1925_A_note_on_the_kinetics_of_enzyme_action

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
doi I D ap bj0190338 ep

Celestial Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CelestialMechanics

branch of astronomy that deals with the motions of objects in outer space
belongs to
Research Field c
has facts
generalized by field op Astronomy ni
generalized by field op Classical Mechanics ni
description ap "Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data."@en
wikidata I D ap Q184274 ep

Center Of Provinceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CenterOfProvince

centers of the respective provinces
belongs to
Quantity c

Centrifugal Distortion Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CentrifugalDistortionConstant

distortion of a molecule caused by the centrifugal force produced by rotation
belongs to
Quantity c
has facts
description ap "This distortion leads to changes in bond distance and angles, affecting the rotational spectrum."@en

Change In Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInLength

difference between the current and the original (equilibrium) length
belongs to
Quantity c
has facts
generalized by quantity op Length ni
wikidata I D ap Q91308394 ep

Change In Opinions Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfIndividuals

opinion adaption of individuals over time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Interaction Force ni
contains quantity op Noise Strength ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Opinion Vector of Influencers ni
contains quantity op Opinion Vector of Media ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$dx_i(t) = F_i(\mathbf{x}, \mathbf{y}, \mathbf{z}, t)dt + \sigma dW_i(t)$"^^La Te X ep
in defining formulation dp "$F_i(t)$, Interaction Force"^^La Te X ep
in defining formulation dp "$W_i(t)$, Wiener Process"^^La Te X ep
in defining formulation dp "$\mathbf{x}(t)$, Opinion Vector of Individuals"^^La Te X ep
in defining formulation dp "$\mathbf{y}(t)$, Opinion Vector of Media"^^La Te X ep
in defining formulation dp "$\mathbf{z}(t)$, Opinion Vector of Influencers"^^La Te X ep
in defining formulation dp "$\sigma$, Noise Strength"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Individuals i = 1,...,N adapt their opinions in time according to this stochastic differential equation (SDE)"@en

Change In Opinions Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfInfluencers

opinion adaption of influencers over time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Influencers ni
contains quantity op Inertia Parameter For Opinion Changes Of Influencers ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\gamma d z_l(t)=\left(\hat{x}_l(t)-z_l(t)\right) d t+\hat{\sigma} d \hat{W}_l(t)$"^^La Te X ep
in defining formulation dp "$\gamma$, Inertia Parameter For Opinion Changes Of Influencers"^^La Te X ep
in defining formulation dp "$\hat{W}_l$, Wiener Process"^^La Te X ep
in defining formulation dp "$\hat{\sigma}$, Noise Strength"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$z_l(t)$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "Influencers l= 1,. . . , L slowly change their opinions in the direction of their average followership according to this Stochastic differential equation"@en

Change In Opinions Of Influencers In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfInfluencrsInThePartialFieldModel

opinion adaption of influencers over time in the partial mean field model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni
contains quantity op Inertia Parameter For Opinion Changes Of Influencers ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\gamma d z_l(t)=\left(\hat{x}_l(t)-z_l(t)\right) d t+\hat{\sigma} d \hat{W}_l(t)$"^^La Te X ep
in defining formulation dp "$\gamma$, Inertia Parameter For Opinion Changes Of Influencers"^^La Te X ep
in defining formulation dp "$\hat{W}_l$, Wiener Process"^^La Te X ep
in defining formulation dp "$\hat{\sigma}$, Noise Strength"^^La Te X ep
in defining formulation dp "$\hat{x}_l$, Average Opinion Of Followers Of Influencers In The Partial Field Model"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$z_l$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
description ap "Stochastic Differential equation describing the change in opinions of a given Influencer in the partial field opinion model"@en

Change In Opinions Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfMedia

opinion adaption of media agents over time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Media ni
contains quantity op Inertia Parameter For Opinion Changes Of Media ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\Gamma d y_m(t)=\left(\tilde{x}_m(t)-y_m(t)\right) d t+\tilde{\sigma} d \tilde{W}_m(t)$"^^La Te X ep
in defining formulation dp "$\Gamma$, Inertia Parameter For Opinion Changes Of Media"^^La Te X ep
in defining formulation dp "$\tilde{W}_m$, Wiener Process"^^La Te X ep
in defining formulation dp "$\tilde{\sigma}$, Noise strength"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y_m(t)$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "Media agents m = 1,...,M slowly adapt their opinions according to this stochastic differential equation such that media agents are drawn in the direction of the average opinion of their followers."@en

Change In Opinions Of Media In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfMediaInThePartialFieldModel

opinion adaption of media agents over time in the partial mean field model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Media In The Partial Mean Field Model ni
contains quantity op Inertia Parameter For Opinion Changes Of Media ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\Gamma d y_m(t)=\left(\tilde{x}_m(t)-y_m(t)\right) d t+\tilde{\sigma} d \tilde{W}_m(t)$"^^La Te X ep
in defining formulation dp "$\Gamma$, Inertia Parameter For Opinion Changes Of Media"^^La Te X ep
in defining formulation dp "$\tilde{W}_m$, Wiener Process"^^La Te X ep
in defining formulation dp "$\tilde{\sigma}$, Noise strength"^^La Te X ep
in defining formulation dp "$\tilde{x}_m$, Average Opinion Of Followers Of Media In The Partial Field Model"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y_m$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
description ap "Stochastic Differential equation describing the change in opinions of a given medium in the partial field opinion model"@en

Charge Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChargeTransport

transport of electric charge
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni

Charge Transport Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChargeTransportModel

simple mathematical model for the transport of electric charge
belongs to
Mathematical Model c
has facts
contains formulation op Ohm Equation ni
models op Charge Transport ni

Chemical Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChemicalPotential

energy that can be absorbed or released due to a change of the particle number of a given species
belongs to
Quantity c
has facts
generalizes quantity op External Chemical Potential ni
description ap "e.g. in a chemical reaction or phase transition."@en
wikidata I D ap Q737004 ep

Chemical Reaction Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChemicalReactionKinetics

study of the rates of chemical reactions
belongs to
Research Field c
has facts
generalized by field op Physical Chemistry ni
generalizes field op Enzyme Kinetics ni
wikidata I D ap Q209082 ep

Civil Engineeringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Civil_Engineering

engineering discipline specializing in design, construction and maintenance of the built environment
belongs to
Research Field c
has facts
wikidata I D ap Q77590 ep

Classical Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalAcceleration

rate at which the magnitude and/or direction of velocity changes with time
belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni
wikidata I D ap Q11376 ep

Classical Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalApproximation

classical dynamics as an approximation to quantum mechanics
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Classical Dynamics Model ni
contained as assumption in op Classical Hamilton Equations ni
contained as assumption in op Classical Newton Equation ni
contains quantity op de Broglie Wavelength ni
defining formulation dp "$\lambda \ll L$"^^La Te X ep
in defining formulation dp "$L$, typical dimension of the system"^^La Te X ep
in defining formulation dp "$\lambda$, de Broglie Wavelength"^^La Te X ep

Classical Brownian Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalBrownianEquation

special case of an equation of motion where no average acceleration takes place
belongs to
Mathematical Formulation c
has facts
contains quantity op Boltzmann Constant ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Diffusion Coefficient ni
contains quantity op Temperature ni
contains quantity op Time ni
contains quantity op White Noise ni
generalized by formulation op Classical Langevin Equation ni
defining formulation dp "$\frac{\text{d}}{\text{d}t}q = - \frac{D}{k_\text{B} T} F(q) + \sqrt{2 D} R(t)$"^^La Te X ep
in defining formulation dp "$D$, Diffusion Constant"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$R(t)$, White Noise"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$k_\text{B}$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
alt Label ap "Langevin Equation Without Inertia."@en
alt Label ap "Overdamped Langevin Equation"@en
wikidata I D ap Q178036 ep
wikidata I D ap Q4976526 ep

Classical Brownian Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalBrownianModel

mathematical model for describing molecular systems in the diffusive regime
belongs to
Mathematical Model c
has facts
contains formulation op Classical Brownian Equation ni
generalized by model op Classical Langevin Model ni
models op Molecular Dynamics ni
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
alt Label ap "overdamped Langevin dynamics"@en
wikidata I D ap Q4976526 ep

Classical Density (Phase Space)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalDensityPhaseSpace

probability that the system will be found in the infinitesimal phase space volume
belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
generalized by quantity op Quantum Density Operator ni

Classical Dynamics Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalDynamicsModel

mathematical model of a system of point masses, subject to forces deriving from some potential energy function
belongs to
Mathematical Model c
has facts
contains formulation op Classical Hamilton Equations ni
contains formulation op Classical Newton Equation ni
contains initial condition op Initial Classical Momentum ni
contains initial condition op Initial Classical Position ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean

Classical Fokker Planck Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalFokkerPlanckEquation

partial differential equation describing the dynamics of a probability density of the velocity of a particle under the influence of drag forces and random forces
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Position ni
contains quantity op Control System Input ni
contains quantity op Diffusion Coefficient ni
contains quantity op Drift (Velocity) ni
contains quantity op Probability Distribution ni
contains quantity op Time ni
similar to formulation op Classical Brownian Equation ni
similar to formulation op Classical Langevin Equation ni
defining formulation dp "$\frac{\partial}{\partial t} p(x, t) = -\frac{\partial}{\partial x}\left[(\mu(x, t)-u) p(x, t)\right] + \frac{\partial^2}{\partial x^2}\left[D(x, t) p(x, t)\right]$"^^La Te X ep
in defining formulation dp "$D$, Diffusion constant"^^La Te X ep
in defining formulation dp "$\mu$, Drift"^^La Te X ep
in defining formulation dp "$p$, Probability Distribution"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u_t$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Classical Position"^^La Te X ep
description ap "For vanishing drift and constant diffusion, the Fokker Planck equation yield's Fick's first law of diffusion."@en
description ap "Note the external forcing which connects the FPE to the model order reduction and/or optimal control tasks."@en
wikidata I D ap Q891766 ep

Classical Fokker Planck Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalFokkerPlanckModel

dynamics of a probability density of the velocity of a particle under the influence of drag forces and random forces
belongs to
Mathematical Model c
has facts
applied by task op Balanced Truncation (Bi-linear) ni
applied by task op H2 Optimal Approximation (Bi-linear) ni
applied by task op Optimal Control ni
contains formulation op Classical Fokker Planck Equation ni
similar to model op Classical Brownian Model ni
similar to model op Classical Langevin Model ni
wikidata I D ap Q891766 ep

Classical Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalForce

vector quantity that describes the ability of an action to modify the movement and shape of an object
belongs to
Quantity c
has facts
contained in formulation op Classical Newton Equation ni
generalized by quantity op Force ni
wikidata I D ap Q11402 ep

Classical Hamilton Equationsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonEquations

classical equations of motion for systems described by a classical Hamilton function specifying the total energy
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains quantity op Classical Hamilton Function ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
generalized by formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Classical Newton Equation ni
defining formulation dp "$\begin{align} \frac{\mathrm{d}\boldsymbol{q}}{\mathrm{d}t} &=& +\frac{\partial \mathcal{H}}{\partial \boldsymbol{p}} \\ \frac{\mathrm{d}\boldsymbol{p}}{\mathrm{d}t} &=& -\frac{\partial \mathcal{H}}{\partial \boldsymbol{q}} \end{align}$"^^La Te X ep
in defining formulation dp "$H$, Classical Hamilton Function"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena."@en
wikidata I D ap Q1115699 ep

Classical Hamilton Equations (Leap Frog)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonEquationsLeapFrog

leap frog scheme for time-discretization of Hamilton's equations of motion
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Forward Method ni
contains quantity op Classical Force ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
contains quantity op Time Step ni
discretizes formulation op Classical Hamilton Equations ni
similar to formulation op Schrödinger Equation (Strang-Marchuk) ni
defining formulation dp "$\begin{align} p(t+\tau/2) &=& p(t)+\tau F(q(t))/2 \\ q(t+\tau) &=& q(t)+\tau p(t+\tau/2)/m \\ p(t+\tau) &=& p(t+\tau/2)+\tau F(q(t+\tau))/2 \end{align}$"^^La Te X ep
in defining formulation dp "$F$, Classical Forces"^^La Te X ep
in defining formulation dp "$\tau$, Time Step"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "false"^^boolean

Classical Hamilton Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonFunction

function of generalized positions and momenta in Hamiltonian mechanics, specifying the total energy of a system
belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
generalized by quantity op Energy ni
wikidata I D ap Q360356 ep

Classical Langevin Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLangevinEquation

same as (classical) Newton's equation of motion, but with additional terms for friction|damping and for stochastic collisions added
belongs to
Mathematical Formulation c
has facts
contains quantity op Boltzmann Constant ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Friction Coefficient ni
contains quantity op Mass ni
contains quantity op Temperature ni
contains quantity op Time ni
contains quantity op White Noise ni
generalizes formulation op Classical Newton Equation ni
defining formulation dp "$M\frac{\mathrm{d^2}}{\mathrm{d}t^2} \vec{q} = F(q) - \gamma \frac{\mathrm{d}}{\mathrm{d}t}{q} + \sqrt{2 \gamma k_B T} R(t)$"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$M$, Mass"^^La Te X ep
in defining formulation dp "$R(t)$, White Noise"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\gamma$, Friction Coefficient"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "Note that a Langevin equation can be reformulated as a Fokker–Planck equation governing a probability distribution"@en
wikidata I D ap Q584537 ep

Classical Langevin Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLangevinModel

mathematical model typically used to describe the dynamics of systems subject to a combination of deterministic and fluctuating forces
belongs to
Mathematical Model c
has facts
contains formulation op Classical Langevin Equation ni
generalizes model op Classical Dynamics Model ni
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom only implicitly, i.e., by the use of stochastic differential equations."@en
wikidata I D ap Q6485978 ep

Classical Liouville Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLiouvilleEquation

partial differential equation for the that time rate of change of density of points in phase space
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains assumption op Classical Approximation ni
contains assumption op Nonrelativistic Approximation ni
contains quantity op Classical Density (Phase Space) ni
contains quantity op Classical Hamilton Function ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
contains quantity op Time ni
generalizes formulation op Classical Hamilton Equations ni
defining formulation dp "$\frac{d\rho}{dt}=\frac{\partial\rho}{\partial t}+\sum_{i=1}^n\left(\frac{\partial\rho}{\partial q_i}\dot{q}_i+\frac{\partial\rho}{\partial p_i}\dot{p}_i\right)$"^^La Te X ep
in defining formulation dp "$H$, Classical Hamilton Function"^^La Te X ep
in defining formulation dp "$\rho$, Classical Density (Phase Space)"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Consider a Hamiltonian dynamical system with canonical coordinates and conjugate momenta. Then the phase space distribution determines the probability that the system will be found in the infinitesimal phase space volume."@en
description ap "Note the similarity with the quantum Liouville (von Neumann) equation where the Poisson brackets {.,.} are replaced by commutator brackets [.,.]"@en
wikidata I D ap Q766722 ep

Classical Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMechanics

sub-field of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces
belongs to
Research Field c
has facts
generalized by field op Continuum Mechanics ni
wikidata I D ap Q11397 ep

Classical Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMomentum

momentum of a point particle in classical mechanics
belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
generalized by quantity op Momentum ni
wikidata I D ap Q41273 ep

Classical Momentum (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMomentumDefinition

momentum of a point particle in classical mechanics
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Classical Velocity ni
contains quantity op Mass ni
defines op Classical Momentum ni
defining formulation dp "$p \equiv mv$"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
wikidata I D ap Q41273 ep

Classical Newton Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalNewtonEquation

fundamental equation in classical mechanics that describe the motion of objects under the influence of forces
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
generalized by formulation op Classical Hamilton Equations ni
defining formulation dp "$\frac{\mathrm{d^2}}{\mathrm{d}t^2} \vec{q} = \vec{F} / m$"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "when a body is acted upon by a force, the time rate of change of its momentum equals the force"@en
wikidata I D ap Q2397319 ep

Classical Newton Equation (Stoermer Verlet)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalNewtonEquationStoermerVerlet

sympletic, reversible time-discretization of Newton's equations of motion
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
contains quantity op Time Step ni
discretizes formulation op Classical Newton Equation ni
similar to formulation op Schrödinger Equation (Second Order Differencing) ni
defining formulation dp "$q(t+\tau)=2q(t)-q(t-\tau)+\tau^2F(q(t))/M$"^^La Te X ep
in defining formulation dp "$F$, Classical Forces"^^La Te X ep
in defining formulation dp "$\tau$, Time Step"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "Originally discovered already by Newton: Essentially a symmetric (and symplectic!) combination of Euler forward and backward methods"@en
doi I D ap Phys Rev.159.98 ep
wikidata I D ap Q5475314 ep

Classical Positionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalPosition

position of a point particle in classical mechanics
belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
contained in formulation op Classical Newton Equation ni
generalized by quantity op Length ni

Classical Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalVelocity

velocity of a point particle in classical mechanics
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni

Closed System Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClosedSystemApproximation

assuming that a quantum system does not interact with its environment
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Schrödinger Equation (Time Dependent) ni
contained as assumption in op Schrödinger Equation (Time Independent) ni
contains quantity op Quantum Damping Rate ni
defining formulation dp "$\gamma \rightarrow 0$"^^La Te X ep
in defining formulation dp "$\gamma$, Quantum Damping Rate"^^La Te X ep
description ap "Note that dissipation as well as dephasing (or more formally: the corresponding rates in the Lindblad equation) are neglected."@en
wikidata I D ap Q4476520 ep

Coefficient Scaling Infectious To Exposedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CoefficientScalingInfectiousToExposed

coefficient scales the number of infectious to estimate the number of exposed individuals
belongs to
Quantity c

Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CompetitiveInhibitionConstantUniUniReactionReversibleInhibition

constant for the competitive inhibition in an uni uni reaction
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean

Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CompetitiveInhibitionConstantUniUniReactionReversibleInhibitionDefinition

constant for the competitive inhibition in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Reaction Rate Constant ni
defines op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$K_{ic} \equiv \frac{k_{-3}}{k_3}$"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "definition of the competitive inhibition constant in an uni uni reaction with reversible Inhibition"@en

Complex Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComplexDimensionless

number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q11567 ep

Complexed Enzyme Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComplexedEnzymeConcentration

amount of enzyme that is bound to its substrate, product, or intermediates in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
generalized by quantity op Enzyme Concentration ni

Computational Social Scienceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComputationalSocialScience

academic sub-discipline concerned with computational approaches to the social sciences
belongs to
Research Field c
has facts
wikidata I D ap "https://www.wikidata.org/wiki/Q16909867"

Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Concentration

abundance of a constituent divided by the total volume of a mixture
belongs to
Quantity Kind c
has facts
qudt I D ap Amount Of Substance Concentration.html ep
wikidata I D ap Q3686031 ep

Condition For Positive Solutions In The Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSIModel

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$max_i\{\textstyle\sum_{k=1}^K\alpha_{ik}\Delta t N^k/N^i \} \leq 1$"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSIRModel

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$max_i\{\textstyle\sum_{k=1}^K\alpha_{ik}\Delta t N^k/N^i, \gamma_i \Delta t \} \leq 1$"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSISModel

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains formulation op Between Population Contact Rate Equation ni
contains quantity op Between Population Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\max_{i} \{a_i, \gamma_i \Delta t\} \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSIRModel

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$max\{\gamma \Delta t, \alpha \Delta t \} \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "The time step must be less than the average time required for a successful contact and less than the average infectious period."@en

Condition For Positive Solutions In The SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSIRModelWithBirthsAndDeaths

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$(\gamma +\beta) \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSISModel

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\gamma \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIS Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSISModelWithBirthsAndDeaths

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$(\gamma + \beta) \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition To Keep Susceptibles Positiveni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionToKeepSusceptiblesPositive

posiive solution consraint
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is time-continuous dp "false"^^boolean
description ap "Necessary and sufficient condition to ensure that S_n, is positive for all initial conditions (and I_n < N). Implies that the time step At must be less than the average time required for a successful contact."@en

Conservation Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConservationLaw

scientific law regarding conservation of a physical property
belongs to
Mathematical Formulation c
has facts
wikidata I D ap Q205805 ep

Conservation of City Numbersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConservationOfCityNumbers

conservation of city numbers in every region m
belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Cities ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Time ni
generalized by formulation op Conservation Law ni
defining formulation dp "$i_m(t) = P_m - s_m(t)$"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$i_m(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Constant Population Sizeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConstantPopulationSize

total population size remains constant
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
generalized by formulation op Conservation Law ni
defining formulation dp "$S_n + I_n \approx N, n = 1,2,...$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is time-continuous dp "false"^^boolean

Contact Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetwork

contact network for regions
belongs to
Quantity c
has facts
defined by op Contact Network (Definition) ni
is dimensionless dp "true"^^boolean

Contact Network (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetworkDefinition

contact network for regions m and n
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Number of Cities ni
contains quantity op Region ni
contains quantity op Region Connectivity ni
defining formulation dp "$G_{m,n} \equiv \begin{cases} \frac{W_{m,n}}{P_m} + \frac{W_{n,m}}{P_n} \quad &\text{for} \quad m \neq n \\ \frac{W_{m,m}}{P_m} \quad &\text{for} \quad m = n \end{cases}$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$P$, Number of Cities"^^La Te X ep
in defining formulation dp "$W$, Region Connectivity"^^La Te X ep
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
description ap "definition of contact network"@en

Contact Network (Time-dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeDependentContactNetwork

tuple of spreading rate and contact network interpreted as time-evolving contact network
belongs to
Quantity c
has facts
defined by op Contact Network (Time-dependent, Definition) ni
is dimensionless dp "true"^^boolean

Contact Network (Time-dependent, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeDependentContactNetworkDefinition

tuple of spreading rate and contact network interpreted as time-evolving contact network
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\sigma \equiv (G,\alpha)$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$\alpha$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Contact Network Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetworkConstraint

constraints applying to contact network
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Region ni
defining formulation dp "$\forall \, m\ne n,\, 0\le G_{m,n} \le 2, \text { and } 0\le G_{m,m} \le 1$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Contact Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactRate

average number of individuals with whom an infectious individual makes sufficient contact (to pass infection) during a unit time
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "false"^^boolean

Contact Rate Between Two Groupsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactRateBetweenTwoGroups

average number of contacts per unit time of an infective in a group with individuals in another group
belongs to
Quantity c

Continuity Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquation

equation constraining a quantity to flow only via adjacent locations; can express a locality principle
belongs to
Mathematical Formulation c
has facts
contains quantity op Particle Flux Density ni
contains quantity op Particle Number Density ni
generalized by formulation op Conservation Law ni
generalizes formulation op Continuity Equation For Electrons ni
generalizes formulation op Continuity Equation For Holes ni
defining formulation dp "$ {\delta \rho / \delta t} + \nabla \cdot j = 0$"^^La Te X ep
in defining formulation dp "$\rho$, Particle Number Density"^^La Te X ep
in defining formulation dp "$j$, Particle Flux Density"^^La Te X ep
wikidata I D ap Q217219 ep

Continuity Equation For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForElectrons

continuity equation for electrons; for use in semiconductor physics
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Current Density Of Electrons ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Recombination Of Electron Hole Pairs ni
generalized by formulation op Continuity Equation ni
defining formulation dp "$\nabla \cdot j_n=qR(\psi,\phi_n,\phi_p)$"^^La Te X ep
in defining formulation dp "$R$, Recombination Of Electron Hole Pairs"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_n$, Electric Current Density Of Electrons"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Continuity Equation For Electrons (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForElectronsFiniteVolume

used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
discretizes formulation op Continuity Equation For Electrons ni
defining formulation dp "$j_{n;k,k+1}-j_{n;k-1,k}=qR(\psi_k,\phi_{n;k},\phi_{p;k})|\omega_k|$"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
is space-continuous dp "false"^^boolean

Continuity Equation For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForHoles

continuity equation for holes; for use in semiconductor physics
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Current Density Of Holes ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Recombination Of Electron Hole Pairs ni
generalized by formulation op Continuity Equation ni
defining formulation dp "$\nabla \cdot j_p=-qR(\psi,\phi_n,\phi_p)$"^^La Te X ep
in defining formulation dp "$R$, Recombination of Electron Hole Pairs"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_p$, Electric Current Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Continuity Equation For Holes (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForHolesFiniteVolume

used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
discretizes formulation op Continuity Equation For Holes ni
defining formulation dp "$j_{p;k,k+1}-j_{p;k-1,k}=-qR(\psi_k,\phi_{n;k},\phi_{p;k})|\omega_k|$"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
is space-continuous dp "false"^^boolean

Continuity of the Normal Mass Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityOfTheNormalMassFlux

continuity condition to be used as boundary condition within Stokes Darcy hybrid models
belongs to
Mathematical Formulation c
has facts
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Fluid Velocity (Porous Medium) ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$[v \cdot n]^{pm} = -[v \cdot n]^{ff} \quad \mathrm{on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
in defining formulation dp "$v^{pm}$, Fluid Velocity (Porous Medium)"^^La Te X ep

Continuity of the Normal Stressesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityOfTheNormalStresses

continuity condition to be used as boundary condition within Stokes Darcy hybrid models
belongs to
Mathematical Formulation c
has facts
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Viscous Stress ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$n \cdot [(p I-\tau)n]^{ff} = [p]^{pm} \quad \mathrm{on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$\tau$, Fluid Viscous Stress"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep

Continuous Rate of Change of Infectious in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSIModel

rate of change of infectious individuals in the continuous-time SI model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
discretized by formulation op Susceptibles At Time Step n+1 in The Discrete SI Model ni
defining formulation dp "$\frac{d I}{d t}=\frac{\alpha}{N} S I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population SIze"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Infectious in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSIRModel

rate of change of infectious individuals in the continuous-time SIR model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d I}{d t} = I \left( \frac{\alpha}{N} S - \gamma \right)$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$,Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Infectious in the SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSISModel

rate of change of infectious individuals in the continuous-time SIS model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d I}{d t} = I \left( \frac{\alpha}{N} S - \gamma \right)$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Removed in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfRemovedInTheSIRModel

rate of change of removed individuals in the continuous-time SIR model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time ni
defining formulation dp "$\frac{d R}{d t} = R + \gamma I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Susceptibles in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSIModel

rate of change of susceptible individuals in the continuous-time SI model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
discretized by formulation op Infectious At Time Step n+1 in the SI Model ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population SIze"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Susceptibles in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSIRModel

rate of change of susceptible individuals in the continuous-time SIR model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I $"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Susceptibles in the SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSISModel

rate of change of susceptible individuals in the continuous-time SIS model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I + \gamma I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousModel

continuous-time model for the spreading of infectious diseases considering susceptible and infectious individuals
belongs to
Mathematical Model c
has facts
discretized by model op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousRemovedModel

continuous-time model for the spreading of infectious diseases considering susceptible, infectious and recovered/removed individuals
belongs to
Mathematical Model c
has facts
discretized by model op Discrete Susceptible Infectious Removed Model ni
generalizes op Continuous Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean
wikidata I D ap "https://www.wikidata.org/wiki/Q2206263"

Continuous Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousSusceptibleModel

continuous-time model for the spreading of infectious diseases with temporary resistance considering susceptible and infectious individuals
belongs to
Mathematical Model c
has facts
discretized by op Discrete Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean
wikidata I D ap "https://www.wikidata.org/wiki/Q2351772"

Continuum Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuumMechanics

branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass
belongs to
Research Field c
has facts
contains problem op Flow in Porous Media ni
contains problem op Free Flow Coupled to Porous Media Flow ni
contains problem op Free Flow of an Incompressible Fluid ni
wikidata I D ap Q193463 ep

Control System Durationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemDuration

time after which a (optimal) control should have reached the target
belongs to
Quantity c

Control System Initialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInitial

initial value for the state vector of a control system
belongs to
Quantity c

Control System Initial (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInitialReduced

initial value for the state vector of a control system; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Control State ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$\tilde{x}_0=T^{-1}x_0$"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$x_0$, Initial Control State"^^La Te X ep

Control System Inputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInput

input to a control system
belongs to
Quantity c

Control System Input Bilinearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputBilinear

bilinear input equation for control systems
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Control System Model (Bilinear) ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
generalizes formulation op Control System Input Linear ni
generalizes formulation op Quantum Lindblad Equation ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\dot{x}(t)=(A+u(t)N)x(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep

Control System Input Bilinear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputBilinearReduced

bilinear input equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Input Bilinear ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
contains quantity op Control System State (Reduced) ni
contains quantity op Time ni
generalizes formulation op Control System Input Linear (Reduced) ni
defining formulation dp "$\dot{\tilde{x}}(t)=(\tilde{A}+u(t)\tilde{N})\tilde{x}(t)+\tilde{B}u(t)$"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{N}$, Control System Matrix N (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep

Control System Input Linearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputLinear

linear input equation for control systems
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System State ni
contains quantity op Time ni
generalizes formulation op Quantum Lindblad Equation ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\dot{x}(t)=Ax(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep

Control System Input Linear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputLinearReduced

linear input equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Input Linear ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System State (Reduced) ni
contains quantity op Time ni
defining formulation dp "$\dot{\tilde{x}}(t)=\tilde{A}\tilde{x}(t)+\tilde{B}u(t)$"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep

Control System Lagrange Multiplierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemLagrangeMultiplier

method to solve constrained optimization problems for control systems
belongs to
Quantity c

Control System Matrix Ani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixA

homogeneous part of (linear) input equation for control systems
belongs to
Quantity c

Control System Matrix A (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixAReduced

homogeneous part of (linear) input equation for control systems; after model order reduction
belongs to
Quantity c
has facts
defined by op Control System Matrix A (Reduced, Definition) ni

Control System Matrix A (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixAReducedDefinition

homogeneous part of (linear) input equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix A (Reduced) ni
defining formulation dp "$\tilde{A} \equiv T^{-1}AT$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep

Control System Matrix Bni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixB

inhomogeneous part of (linear) input equation for control systems
belongs to
Quantity c

Control System Matrix B (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixBReduced

inhomogeneous part of (linear) input equation for control systems; after model order reduction
belongs to
Quantity c
has facts
defined by op Control System Matrix B (Reduced, Definition) ni

Control System Matrix B (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixBReducedDefinition

inhomogeneous part of (linear) input equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix B (Reduced) ni
defining formulation dp "$\tilde{B} \equiv T^{-1}BT$"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep

Control System Matrix Cni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixC

linear part of output equation for control systems
belongs to
Quantity c

Control System Matrix C (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixCReduced

linear part of output equation for control systems; after model order reduction
belongs to
Quantity c
has facts
contained in formulation op Control System Output Linear (Reduced) ni
defined by op Control System Matrix C (Reduced, Definition) ni

Control System Matrix C (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixCReducedDefinition

linear part of output equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix C (Reduced) ni
defining formulation dp "$\tilde{C} \equiv CT$"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep

Control System Matrix Dni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixD

quadratic part of output equation for control systems
belongs to
Quantity c

Control System Matrix D (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixDReduced

quadratic part of output equation for control systems; after model order reduction
belongs to
Quantity c
has facts
contained in formulation op Control System Output Quadratic (Reduced) ni
defined by op Control System Matrix D (Reduced, Definition) ni

Control System Matrix D (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixDReducedDefinition

quadratic part of output equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix D ni
contains quantity op Control System Matrix D (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix D (Reduced) ni
defining formulation dp "$\tilde{D} \equiv T^{-1}DT$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{D}$, Control System Matrix D (Reduced)"^^La Te X ep

Control System Matrix Nni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixN

bilinear part of input equation for control systems
belongs to
Quantity c

Control System Matrix N (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixNReduced

bilinear part of input equationfor control systems; after model order reduction
belongs to
Quantity c
has facts
defined by op Control System Matrix N (Reduced, Definition) ni

Control System Matrix N (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixNReducedDefinition

bilinear part of input equationfor control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix N ni
contains quantity op Control System Matrix N (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix N (Reduced) ni
defining formulation dp "$\tilde{N} \equiv T^{-1}NT$"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{N}$, Control System Matrix N (Reduced)"^^La Te X ep

Control System Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModel

branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs, that modify their behavior
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
generalizes model op Control System Model (Bilinear) ni
models op Molecular Spectroscopy (Transient) ni
models op Spin Qbit Shuttling ni
description ap "In general, there are there are two types of controls: open-loop control (feedforward), and closed-loop control (feedback). In many applications of practical relevance, the state vector x is very high-dimensional, even though input u and output y may be low-dimensional"@en
wikidata I D ap Q6501221 ep
wikidata I D ap Q959968 ep

Control System Model (Bilinear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModelBilinear

control system with bi-linear input equation
belongs to
Mathematical Model c
has facts
contains initial condition op Initial Control State ni
generalizes model op Control System Model (Linear) ni
models op Molecular Spectroscopy (Transient) ni
models op Spin Qbit Shuttling ni

Control System Model (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModelLinear

control system with linear input equation
belongs to
Mathematical Model c

Control System Outputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutput

output from a control system
belongs to
Quantity c

Control System Output Linearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputLinear

linear output equation for control systems
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Balanced Truncation (Bi-linear) ni
contained as formulation in op Control System Model (Bilinear) ni
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Output ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$y(t)=Cx(t)$"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep

Control System Output Linear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputLinearReduced

linear output equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Output Linear ni
contains quantity op Control System Output ni
contains quantity op Time ni
defining formulation dp "$y(t)=\tilde{C}\tilde{x}(t)$"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep

Control System Output Quadraticni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputQuadratic

quadratic output equation for control systems
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Balanced Truncation (Bi-linear) ni
contained as formulation in op Control System Model (Bilinear) ni
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Matrix D ni
contains quantity op Control System Output ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$y(t)=x^{\dagger}(t)Dx(t)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep

Control System Output Quadratic (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputQuadraticReduced

quadratic output equation for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Output Quadratic ni
contains quantity op Control System Output ni
contains quantity op Time ni
defining formulation dp "$y(t)=\tilde{x}^{\dagger}(t)\tilde{D}\tilde{x}(t)$"^^La Te X ep
in defining formulation dp "$\tilde{D}$, Control System Matrix D (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep

Control System Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemState

state vector of a dynamical system for control systems
belongs to
Quantity c

Control System State (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemStateReduced

state vector of a dynamical system for control systems; after model order reduction
belongs to
Quantity c
has facts
contained in formulation op Control System Output Linear (Reduced) ni
contained in formulation op Control System Output Quadratic (Reduced) ni
defined by op Control System State (Reduced, Definition) ni

Control System State (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemStateReducedDefinition

state vector of a dynamical system for control systems; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System State ni
contains quantity op Control System State (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$\tilde{x} \equiv T^{-1}x$"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep

Control System Time Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemTimeEvolution

computing the time evolution of a control system, for given initial state and given control , yielding output as a function of time
belongs to
Computational Task c
has facts
applies model op Control System Model ni
generalizes task op Control System Time Evolution (Bi-linear) ni

Control System Time Evolution (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemTimeEvolutionLinear

computing the time evolution of a control system with linear input equation
belongs to
Computational Task c
has facts
applies model op Control System Model (Linear) ni
contains formulation op Control System Input Linear ni
contains formulation op Control System Output Linear ni
contains initial condition op Initial Control State ni
contains input op Control System Input ni
contains output op Control System Output ni
contains parameter op Control System Matrix A ni
contains parameter op Control System Matrix B ni
contains parameter op Control System Matrix C ni

Control Volumeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlVolume

mathematical abstraction employed in mathematical models of continuum mechanics and thermodynamics used within finite volume discretizations
belongs to
Quantity c
has facts
defined by op Control Volume (Definition) ni
description ap "used for example in the Scharfetter-Gummel discretization of the drift diffusion (aka van-Roosbroeck) system"@en
wikidata I D ap Q5165895 ep

Control Volume (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlVolumeDefinition

mathematical abstraction employed in mathematical models of continuum mechanics and thermodynamics used within finite volume discretizations
belongs to
Mathematical Formulation c
has facts
contains quantity op Control Volume ni
contains quantity op Spatial Variable ni
defining formulation dp "$\omega_k \equiv [x_{k-1,k}-x_{k,k+1}]$"^^La Te X ep
in defining formulation dp "$\omega$, Control Volume"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep
description ap "control volume used within finite volume discretizations, e.g. the Scharfetter-Gummel discretization of the van-Roosbroeck system"@en
wikidata I D ap Q234072 ep

Coriolis Coupling Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CoriolisCouplingConstant

description of the interaction between rotational and vibrational motions, e.g., in molecules
belongs to
Quantity c
has facts
doi I D ap Phys Rev.56.680 ep
wikidata I D ap Q7370329 ep

Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Costs

value of money required for e.g. producing, buying or running something
belongs to
Quantity Kind c
has facts
wikidata I D ap Q240673 ep

Costs of Line Conceptni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CostsOfLineConcept

summarized costs of a line concept
belongs to
Quantity c
has facts
generalized by quantity op Costs ni

Costs per Unitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CostsPerUnit

costs per unit of something
belongs to
Quantity c
has facts
generalized by quantity op Costs ni
description ap "Costs per unit of something, e.g. costs per 1km, costs per vehicle, costs per line, costs per edge,..."@en

Coulomb Friction Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Coulomb_Friction_Of_Two_Particles

slipping occurs, if tangential force is high in relation to normal force in the contact of two particles
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "if $F^{T, cons}_{ij}> \mu F_{ij}^N$ then $\mathbf F_{ij}^T = \mu F_{ij}^N \mathbf\xi_{ij}/\lVert \mathbf\xi_{ij}\rVert$"^^La Te X ep
in defining formulation dp "$F_{ij}^{T, cons}=-k_{ij}^T\lVert \mathbf \xi_{ij}\rVert$, conservative part of tangential interaction force"^^La Te X ep

Coupling Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CouplingCurrent

transfer current from one circuit to another
belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni

Cross Sectionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CrossSection

the intersection of a body in 3D space with a plane
belongs to
Quantity c
has facts
generalized by quantity op Area ni
description ap "In geometry and in natural sciences, a cross section is the intersection of a body in 3D space with a plane."@en
wikidata I D ap Q845080 ep

Cundall (1979) A discrete numerical model for granular assembliesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Cundall_1979_Discrete_model_granular_assemblies

publication
belongs to
Publication c
has facts
doi I D ap geot.1979.29.1.47 ep

Current Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensity

amount of charge per unit time that flows through a unit area
belongs to
Quantity c
has facts
generalizes quantity op Electric Current Density Of Electrons ni
generalizes quantity op Electric Current Density Of Holes ni
description ap "The (electric) current density is defined as the amount of charge per unit time that flows through a unit area"@en
wikidata I D ap Q234072 ep

Current Flow in Semiconductor Devicesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentFlowInSemiconductorDevices

flow of electrical charge carriers coupled to electrostatic potential distribution in semiconductor devices
belongs to
Research Problem c
has facts
contained in field op Semiconductor Physics ni

Current Procedural Terminologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentProceduralTerminology

procedure codes
belongs to
Quantity c
has facts
wikidata I D ap Q964984 ep

Darcy Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquation

describing the flow of a fluid through a porous medium
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Darcy Model ni
contains quantity op Fluid Dynamic Viscosity (Porous Medium) ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Velocity (Porous Medium) ni
defining formulation dp "$\begin{align} v^{pm} = -K \mu^{-1} \nabla p^{vm} \\ \nabla \cdot v^{pm} = 0 \end{align}$"^^La Te X ep
in defining formulation dp "$K$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\mu$, Fluid Dynamic Viscosity (Porous Medium)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
in defining formulation dp "$v^{pm}$, Fluid Velocity (Porous Medium)"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model describing the flow of a fluid through a porous medium."@en
wikidata I D ap Q392416 ep

Darcy Equation (Euler Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquationEulerBackward

discretizing the Darcy equation by a first-oder backward Euler scheme in time
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Darcy Equation ni
is time-continuous dp "false"^^boolean

Darcy Equation (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquationFiniteVolume

discretizing the Darcy equation by a finite volume scheme in space
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Darcy Equation ni
is space-continuous dp "false"^^boolean

Darcy Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyModel

mathematical model describing the flow of a fluid through a porous medium
belongs to
Mathematical Model c
has facts
wikidata I D ap Q392416 ep

Darcy Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyModelDiscretized

discretized version of Darcy's model describing the flow of a fluid through a porous medium
belongs to
Mathematical Model c
has facts
contains formulation op Darcy Equation (Euler Backward) ni
contains formulation op Darcy Equation (Finite Volume) ni
discretizes model op Darcy Model ni

Darwin-Howie-Whelan Equation for a strained crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarwinHowieWhelanEquationStrained

simuating TEM images by numerically solving the Darwin–Howie–Whelan equation describing the electron propagation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Dynamical Electron Scattering Model ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$\begin{align} \frac{\mathrm d}{\mathrm d z} \varphi_{\mathbf{g}}(z) &= 2\mathrm{i} \pi \Big(s_{\mathbf{g}} + \frac{\mathrm d}{\mathrm d z}(\mathbf{g}\cdot \mathbf{u}(\mathbf{r}))\Big)\varphi_{\mathbf{g}}(z)+ \mathrm{i} \pi\sum_{\mathbf{h}\in \Lambda^*_m} U_{\mathbf{g-h}}\varphi_{\mathbf{h}}(z)\\ \quad s_g &= -\frac{g\cdot(2k_0+g)}{2n\cdot(k_0+g)} \end{align}$"^^La Te X ep
in defining formulation dp "$U_g$, Electric Potential Fourier Coefficients"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\psi_g$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep
in defining formulation dp "$k_0$, Wave Vector of an Electron"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$s_g$, Excitation Error"^^La Te X ep
in defining formulation dp "$u$, Displacement of Atoms"^^La Te X ep

Darwin-Howie-Whelan Equation for an unstrained crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarwinHowieWhelanEquationNoStrain

simuating TEM images of an unstrained crystal by numerically solving the Darwin–Howie–Whelan equation describing the electron propagation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Dynamical Electron Scattering Model ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
defining formulation dp "$\begin{align*} \frac{\mathrm d}{\mathrm d z} \psi_\mathbf{g}(z) &= 2\mathrm{i} \pi s_\mathbf{g} \psi_\mathbf{g}(z)+ \frac{\mathrm{i} \pi}{\rho_\mathbf{g}}\sum_{\mathbf{h}\in \Lambda^*_m} U_{\mathbf{g-h}}\psi_\mathbf{h}(z)\\ \quad s_g &= -\frac{g\cdot(2k_0+g)}{2n\cdot(k_0+g)} \end{align*}$"^^La Te X ep
in defining formulation dp "$U_g$, Electric Potential Fourier Coefficients"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\psi_g$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep
in defining formulation dp "$k_0$, Wave Vector of an Electron"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$s_g$, Excitation error"^^La Te X ep

de Broglie Wavelengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#deBroglieWavelength

wavelength of matter waves in quantum mechanics
belongs to
Quantity c
has facts
defined by op de Broglie Wavelength (Definition) ni
description ap "playing a crucial role for the wave-particle duality in quantum mechanics."@en
wikidata I D ap Q100981463 ep

de Broglie Wavelength (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#deBroglieWavelengthDefinition

wavelength of matter waves in quantum mechanics
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Planck Constant ni
contains quantity op de Broglie Wavelength ni
defines op de Broglie Wavelength ni
defining formulation dp "$\lambda \equiv \frac{h}{p}$"^^La Te X ep
in defining formulation dp "$\lambda$, de Broglie Wavelength"^^La Te X ep
in defining formulation dp "$h$, Planck Constant"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep

Death Countni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DeathCount

death count, at a given age
belongs to
Quantity c

Decision Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DecisionVariable

vector which is to be decided in integer linear program
belongs to
Quantity Kind c
has facts
generalizes quantity op Binary Decision Variable ni

Demographyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Demography

statistical and theoretical study of populations: size, composition, and how they change through fertility, mortality, and migration
belongs to
Research Field c
has facts
contains problem op Mortality Modeling ni
mardi I D ap Item: Q116324 ep
wikidata I D ap Q37732 ep

Denoising for Improved Parametric MRI of the Kidneyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DenoisingForImprovedParametricMRIOfTheKidney

denoising for improved parametric MRI (magnetic resonance imaging) of the kidney
belongs to
Computational Task c
has facts
applies model op Gaussian Noise Model ni
contains formulation op Non-Local Means ni
doi I D ap 978 1 0716 0978 1 34 ep

Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Density

mass per volume of a substance
belongs to
Quantity Kind c
has facts
alt Label ap "Specific Mass"@en
alt Label ap "Volumetric Mass Density"@en
qudt I D ap Density ep
wikidata I D ap Q29539 ep

Density Fraction Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityFractionCoefficient

coefficients used in the definition of the density fractions
belongs to
Quantity c

Density Of Airni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfAir

mass per unit volume of the atmosphere of the planet Earth
belongs to
Quantity c
has facts
generalized by quantity op Density ni
wikidata I D ap Q1511415 ep

Density Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfElectrons

probability density of electrons being somewhere
belongs to
Quantity c
has facts
generalized by quantity op Particle Number Density ni
description ap "For use in semiconductor physics"@en
wikidata I D ap Q905186 ep

Density Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfHoles

probability density of holes being somewhere
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Particle Number Density ni
description ap "For use in semiconductor physics"@en

Density Of States For Conduction Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfStatesForConductionBand

number of allowed states per unit energy range for conduction band
belongs to
Quantity c

Density Of States For Valence Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfStatesForValenceBand

number of allowed states per unit energy range for valence band
belongs to
Quantity c

Detailed Balance Principleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DetailedBalancePrinciple

at thermal equilibrium, each elementary process is in equilibrium with its reverse process
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Lindblad Equation ni
contains quantity op Boltzmann Constant ni
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Temperature ni
defining formulation dp "$\Gamma_{n \to m, m > n} = e^{-\frac{E_m-E_n}{k_BT}} \Gamma_{m \to n, m > n}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\Gamma$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann constant"^^La Te X ep
in defining formulation dp "$m$, Quantum Number"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
description ap "The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions)."@en
wikidata I D ap Q1201087 ep

Diffusion Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionConstant

proportionality constant between the molar flux and the negative value of the gradient in the concentration of the species
belongs to
Quantity c
has facts
contained in formulation op Fick Equation ni
description ap "Diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species."@en
alt Label ap "Diffusivity"@en
alt Label ap "Mass Diffusivity"@en
wikidata I D ap Q604008 ep

Diffusion Coefficient for SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionCoefficient

spatial mixing of the subpopulations
belongs to
Quantity c
has facts
description ap "describes the spatial mixing of the subpopulations and may, in general, depend on the spatial position."@en

Diffusion Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionFlux

solute mass removal rate resulting from diffusion
belongs to
Quantity c
has facts
contained in formulation op Fick Equation ni
generalized by quantity op Particle Flux Density ni

Diffusion Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionsModel

mathematical model describing transport of mass|particles by diffusion
belongs to
Mathematical Model c
has facts
contains formulation op Fick Equation ni
generalized by model op Classical Fokker Planck Model ni

Dirac Delta Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiracDeltaDistribution

generalized function on the real numbers
belongs to
Quantity c
has facts
description ap "Value is zero everywhere except at zero, and whose integral over the entire real line is equal to one."@en

Dirichlet Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryCondition

boundary condition specifying the values that a solution of a differential equation needs to take along the boundaries of a domain
belongs to
Mathematical Formulation c
has facts
alt Label ap "second-type boundary condition"@en
wikidata I D ap Q1193699 ep

Dirichlet Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForElectricPotential

Dirichlet boundary condition for the electric potential at an interface
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Time ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\psi(r,t)|_{\Gamma_k}=\psi_{0}+U_k(t)$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Dirichlet Boundary Condition For Electron Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForElectronFermiPotential

Fermi potential is given by applied external voltages at the Ohmic contacts, e.g. semiconductor-metal interfaces
belongs to
Mathematical Formulation c
has facts
contains quantity op Applied External Voltage ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Electrons ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\phi_n |_{\Gamma_k} = U_k$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep

Dirichlet Boundary Condition For Hole Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForHoleFermiPotential

Fermi potential is given by applied external voltages at the Ohmic contacts, e.g. semiconductor-metal interfaces
belongs to
Mathematical Formulation c
has facts
contains quantity op Applied External Voltage ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Holes ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\phi_n |_{\Gamma_k} = U_k$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep

Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Discrete_Element_Method

family of numerical methods for modeling the behavior of assemblies of discrete particles in contact
belongs to
Mathematical Model c
has facts
invented in op Cundall (1979) A discrete numerical model for granular assemblies ni
description ap "Describes any family of numerical functions for computing the motion and the effects of a large number of small particles. DEM is an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and rock mechanics."@en
wikidata I D ap Q902783 ep

Discrete Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousModel

discrete model for the spreading of infectious diseases considering susceptible and infectious individuals
belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Discrete Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousRemovedModel

discrete model for the spreading of infectious diseases considering susceptible, infectious and recovered/removed individuals
belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
wikidata I D ap Q2206263 ep

Discrete Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousSusceptibleModel

discrete-time model for the spreding of infectious diseases with temporary resistance considering susceptible and infectious individuals
belongs to
Mathematical Model c
has facts
discretizes op Continuous Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
wikidata I D ap Q2351772 ep

Displacementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Displacement

vector that is the shortest distance from the initial (equilibrium) to the final (current) position of a point
belongs to
Quantity c
has facts
generalized by quantity op Length ni
generalizes quantity op Displacement Muscle Tendon ni
generalizes quantity op Displacement Of Atoms ni
description ap "Vector that is the shortest distance from the initial to the final position of a point. In elasticity, displacements typically denote the motion of particles/matter from their equilibrium geometry"@en
qudt I D ap Displacement ep
wikidata I D ap Q190291 ep

Displacement Muscle Tendonni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DisplacementMuscleTendon

displacements of the muscle-tendon connection compared to the stress-free position
belongs to
Quantity c
has facts
generalized by quantity op Change In Length ni
generalized by quantity op Displacement ni
wikidata I D ap Q190291 ep

Displacement Of Atomsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DisplacementOfAtoms

displacement of atoms from their equilibrium positions in a non-rigid molecule or solid
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
generalized by quantity op Length ni

Dissociation Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DissociationConstant

measures the propensity of a larger object to separate (dissociate) reversibly into smaller components
belongs to
Quantity c
has facts
wikidata I D ap Q898254 ep

Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} (1+\frac{K_S}{c_S}) + \frac{K_S c_I}{V_{max,f} K_{ic}*c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{1}{v_0} = \frac{1}{V_{max,f}} (1 + \frac{K_m}{c_S}) + \frac{c_I}{V_{max,f}} (\frac{1}{K_{iu}} + \frac{K_m}{K_{ic}*c_S})$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{1}{v_0} = \frac{1}{V_{max,f}} (1 + \frac{K_m}{c_S}) + \frac{c_I}{V_{max,f}} (\frac{1}{K_{iu}} + \frac{K_m}{K_{ic}*c_S})$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} (1 + \frac{K_S}{c_S}) + \frac{c_I}{V_{max,f} K_{iu}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Doping Profileni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DopingProfile

intentional introduction of impurities into an intrinsic (undoped) semiconductor for the purpose of modulating its electrical, optical and structural properties
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni

Drag Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DragCoefficient

dimensionless parameter to quantify fluid resistance
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q1778961 ep

Drift (Velocity)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Drift

average velocity attained by particles due to external forces
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "Average velocity attained by particles due to external forces, e.g. when subjected to an electric field."@en
wikidata I D ap Q909891 ep

Drift-Diffusion Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DriftDiffusionModel

mathematical model describing the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation
belongs to
Mathematical Model c
has facts
contains boundary condition op Dirichlet Boundary Condition For Electric Potential ni
contains boundary condition op Dirichlet Boundary Condition For Electron Fermi Potential ni
contains boundary condition op Dirichlet Boundary Condition For Hole Fermi Potential ni
contains boundary condition op Neumann Boundary Condition For Electric Potential ni
contains boundary condition op Neumann Boundary Condition For Electron Fermi Potential ni
contains boundary condition op Neumann Boundary Condition For Hole Fermi Potential ni
contains formulation op Boltzmann Approximation For Electrons ni
contains formulation op Boltzmann Approximation For Holes ni
contains formulation op Continuity Equation For Electrons ni
contains formulation op Continuity Equation For Holes ni
contains formulation op Poisson Equation For The Electric Potential ni
discretized by model op Scharfetter-Gummel Scheme ni
models op Current Flow in Semiconductor Devices ni
surveyed in op Koprucki (2017) Numerical methods for drift-diffusion models ni
description ap "The drift-diffusion system describes the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. It became the standard model to describe the current flow in semiconductor devices such as diodes, transistors, LEDs, solar cells and lasers, as well as quantum nanostructures and organic semiconductors."@en
alt Label ap "van Roosbroeck Model"@en
doi I D ap W I A S. P R E P R I N T.2263 ep
doi I D ap 9781315152318 25 ep

Durationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Duration

physical quantity for describing the temporal distance between events
belongs to
Quantity c
has facts
generalized by quantity op Time ni
qudt I D ap Time ep
wikidata I D ap Q2199864 ep

Duration per Unitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DurationPerUnit

duration of an event per specific unit
belongs to
Quantity c
has facts
generalized by quantity op Duration ni
description ap "Duration of an event per specific unit , e.g. duration per 1km, duration per length, duration of line,..."@en

Dynamical Electron Scattering Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DynamicalElectronScatteringModel

quantum-mechanical propagation of electrons through a sample governed by dynamical electron scattering
belongs to
Mathematical Model c
has facts
contains boundary condition op Neumann Boundary Condition (Stress-Free Relaxation) ni
contains formulation op Hooke Law (Linear Elasticity) ni
contains formulation op Momentum Balance Equation ni
generalized by model op Quantum Model (Closed System) ni
description ap "In crystalline solids, e.g. semiconductor nanostructures, it is influenced by spatial variations in the material composition and by local deformations of the lattice due to elastic strain. In order to model TEM images, we need to use elasticity theory to obtain the strain profile and couple this with the equations describing the electron propagation through the sample."@en
doi I D ap s11082 020 02356 y ep

Eadie (1942) The Inhibition of Cholinesterase by Physostigmine and Prostigmineni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Eadie_1942_The_Inhibition_of_Cholinesterase_by_Physostigmine_and_Prostigmine

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni
doi I D ap S0021 9258(18)72452 6 ep

Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductSteadyStateAssumption

equation for uni uni reaction without product following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductIrreversibilityAssumption

equation for uni uni reaction without product following irreversibility assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

equation for uni uni reaction without product following rapid equilibrium assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S (1 + \frac{c_I}{K_{ic}}) \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$v_0 = \frac{V_{max,f}}{1+\frac{c_I}{K_{iu}}} - \frac{K_m (1+\frac{c_I}{K_{ic}})}{1+\frac{c_I}{K_{iu}}} \frac{v_0}{c_S}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$v_0 = \frac{V_{max,f}}{1+\frac{c_I}{K_{iu}}} - \frac{K_m (1+\frac{c_I}{K_{ic}})}{1+\frac{c_I}{K_{iu}}} \frac{v_0}{c_S}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{max,f}}{1 + \frac{c_I}{K_{iu}}} - \frac{K_S}{1 + \frac{c_I}{K_{iu}}} \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Earth Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EarthMass

mass of the planet Earth
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
wikidata I D ap Q25935139 ep

Earth Radiusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EarthRadius

mean distance from the Earth's center to its surface
belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "mean distance from the Earth's center to its surface: A globally-average value is usually considered to be 6,371 kilometres with a 0.3% variability (±10 km)"@en
wikidata I D ap Q1155470 ep

Edgesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Edges

set of all edges in a graph
belongs to
Quantity c
has facts
contained in formulation op Public Transportation Network ni
wikidata I D ap "https://www.wikidata.org/wiki/Q124247109"

Effective Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveConductivity

combined effects of conduction, convection, and radiation heat transfer within an enclosed space or material
belongs to
Quantity c
has facts
generalized by quantity op Electric Conductivity ni
description ap "Effective conductivity refers to the combined effects of conduction, convection, and radiation heat transfer within an enclosed space or material and measures how effectively the medium can transfer heat."@en

Effective Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMass

mass that a particle appears to have when responding to forces
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "The mass that a particle appears to have when responding to forces, or the mass that it seems to have when interacting with other identical particles."@en
qudt I D ap Effective Mass ep
wikidata I D ap Q1064434 ep

Effective Mass (Solid-State Physics)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMassSolidStatePhysics

effective electron masses are deduced from band structure calculations (curvature of bands)
belongs to
Quantity c
has facts
generalized by quantity op Effective Mass ni
description ap "In solid state physics, effective electron masses are deduced from band structure calculations (curvature of bands). In certain cases, these masses can have negative values. Their absolute values are typically found between 0.01 and 10 times the mass of a free electron."@en
wikidata I D ap Q1064434 ep

Effective Mass (Spring-Mass System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMassSpringMassSystem

mass that needs to be added to a particle mass to correctly predict the behavior of the system
belongs to
Quantity c
has facts
generalized by quantity op Effective Mass ni
wikidata I D ap Q3509437 ep

Efficient Numerical Simulation of Soil-Tool Interactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Efficient_Numerical_Simulation_of_Soil-Tool_Interaction

computational method for efficient simulation of soil-tool interactions
belongs to
Research Problem c
has facts
contained in field op Civil Engineering ni
modeled by op Recurrent Neural Network Surrogate for Discrete Element Method ni
studied in op Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni

Egyptologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Egyptology

scientific study of ancient Egypt
belongs to
Research Field c
has facts
mardi I D ap Item: Q6032633 ep
wikidata I D ap Q145903 ep

Eigenstress Of Crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EigenStressOfCrystal

eigenstress of a crystal (stress-free condition) used in theory of elasticity
belongs to
Quantity c
has facts
generalized by quantity op Stress Of Crystal ni

Elastic Stiffness Tensorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElasticStiffnessTensor

fourth-order tensor that describes the relationship between stress and strain in a material
belongs to
Quantity c
has facts
description ap "Elastic Stiffness Tensor, used e.g. in Hook's Law for the elastic deformation of a solid."@en

Electric Capacitanceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Capacitance

ability of a body to store electrical charge
belongs to
Quantity Kind c
has facts
qudt I D ap Capacitance ep
wikidata I D ap Q164399 ep

Electric Chargeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCharge

physical property that quantifies an object's interaction with electric fields
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Charge ep
wikidata I D ap Q1111 ep

Electric Charge Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricChargeDensity

electric charge per volume
belongs to
Quantity c
has facts
generalizes quantity op Density Of Holes ni
similar to quantity op Density Of Electrons ni
similar to quantity op Density Of Holes ni
wikidata I D ap Q69425629 ep

Electric Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricConductivity

physical quantity and property of material describing how readily a given material allows the flow of electric current
belongs to
Quantity Kind c
has facts
description ap "when subject to an electric field, the negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation."@en
qudt I D ap Conductivity.html ep
wikidata I D ap Q4593291 ep

Electric Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrent

base quantity of the International System of Quantities (ISQ), measured in ampere (A)
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Current ep
wikidata I D ap Q29996 ep

Electric Current Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensity

electric current per area of cross section
belongs to
Quantity c
has facts
similar to quantity op Flux Of Electrons ni
similar to quantity op Flux Of Holes ni
wikidata I D ap Q234072 ep

Electric Current Density Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensityOfElectrons

density of electric current of electrons, e.g., in a semiconductor device
belongs to
Quantity c
has facts
defined by op Electric Current Density Of Electrons (Definition) ni
alt Label ap "flux of electrons"@en

Electric Current Density Of Electrons (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensityOfElectronsDefinition

density of electric current of electrons, e.g., in a semiconductor device
belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Electrons ni
contains quantity op Electric Current Density Of Electrons ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Mobility Of Electrons ni
defining formulation dp "$j_n \equiv -q\mu_nn(\psi,\phi_n) \nabla \phi_n$"^^La Te X ep
in defining formulation dp "$\mu_n$, Mobility Of Electrons"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_n$, Electric Current Density Of Electrons"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Electric Current Density Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensityOfHoles

density of electric current of holes, e.g., in a semiconductor device
belongs to
Quantity c
has facts
defined by op Electric Current Density Of Holes (Definition) ni
similar to quantity op Electric Current Density Of Electrons ni
alt Label ap "flux of holes"@en

Electric Current Density Of Holes (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensityOfHolesDefinition

density of electric current of holes, e.g., in a semiconductor device
belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Holes ni
contains quantity op Electric Current Density Of Holes ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Mobility Of Holes ni
defining formulation dp "$j_p \equiv -q\mu_pp(\psi,\phi_p) \nabla \phi_p$"^^La Te X ep
in defining formulation dp "$\mu_p$, Mobility Of Holes"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_p$, Electric Current Density Of Holes"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Electric Dipole Momentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricDipoleMoment

vector physical quantity measuring the separation of positive and negative electrical charges within a system
belongs to
Quantity Kind c
has facts
wikidata I D ap Q735135 ep

Electric Fieldni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricField

vector field representing the force applied to a charged test particle. The electric field is the gradient of the electrostatic potential
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Field Strength ep
wikidata I D ap Q46221 ep

Electric Polarizabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPolarizability

tendency of matter subjected to an electric field to acquire an electric dipole moment
belongs to
Quantity Kind c
has facts
similar to quantity op Permittivity (Dielectric) ni
wikidata I D ap Q869891 ep

Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPotential

electric field is the gradient of the electrostatic potential
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Voltage ni
alt Label ap "Electrostatic Potential"@en
qudt I D ap Electric Potential ep
wikidata I D ap Q55451 ep

Electric Potential Fourier Coefficientsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPotentialFourierCoefficients

coefficients in a Fourier expansion of the electric potential
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
similar to quantity op Electric Potential ni

Electrode Interfacesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectrodeInterfaces

positions of the electrode interfaces
belongs to
Quantity c
has facts
contained in formulation op Dirichlet Boundary Condition For Electric Potential ni
generalized by quantity op Length ni
description ap "Positions of the electrode interfaces. Typically used to specify boundary conditions for electric fields or electron|hole densities in semiconductor-metal interfaces (Ohmic contacts)"@en
wikidata I D ap Q3783831 ep

Electrodynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrodynamics

branch of science concerned with the phenomena of electricity and magnetism
belongs to
Research Field c
is same as
Electromagnetism ni
has facts
same As ep Electromagnetism ni
wikidata I D ap Q377930 ep

Electromagnetic Fields And Wavesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectromagneticFieldsAndWaves

physical fields produced by electrically charged objects
belongs to
Research Problem c
has facts
modeled by op Maxwell Equations Model ni
description ap "Shalva: Given the initial fields E(r, t = 0) and B(r, t = 0), given full charge density ρ(r, t) and the current density j(r, t), find the electric and magnetic fields, E(r, t) and B(r, t)."@en
wikidata I D ap Q177625 ep

Electromagnetismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electromagnetism

branch of science concerned with the phenomena of electricity and magnetism
belongs to
Research Field c
is same as
Electrodynamics ni
has facts
contains problem op Electromagnetic Fields And Waves ni
description ap "branch of theoretical physics that studies consequences of the electromagnetic fields, waves, and forces between electric charges and currents"@en
wikidata I D ap Q377930 ep

Electron Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectronMass

mass of a stationary electron
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "In particle physics, the mass of a stationary electron is one of the fundamental constants of physics."@en
alt Label ap "invariant mass of the electron"@en
qudt I D ap Electron Mass ep
wikidata I D ap Q3814108 ep

Electron Shuttling Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectronShuttlingModel

quantum dynamical model of an electron to be shuttled in a Silicon QuBus device
belongs to
Mathematical Model c
has facts
contains boundary condition op Dirichlet Boundary Condition For Electric Potential ni
contains boundary condition op Neumann Boundary Condition For Electric Potential ni
contains boundary condition op Periodic Boundary Condition For Electric Potential ni
contains formulation op Laplace Equation For The Electric Potential ni
contains formulation op Quantum Hamiltonian (Electric Charge) ni
contains formulation op Quantum Lindblad Equation ni
contains formulation op Schrödinger Equation (Time Dependent) ni
contains formulation op Schrödinger Equation (Time Independent) ni
generalized by model op Control System Model (Bilinear) ni
generalized by model op Quantum Model (Closed System) ni
models op Spin Qbit Shuttling ni
description ap "Quantum dynamical modeling of an electron to be shuttled, governed by the electric potential generated by the clavier (and other) gates in a Silicon QuBus device. Spin and valley states as well as the respective interactions are neglected. Moreover, the current model is limited to the coherent wave packet evolution and disregards the effects of noise and dissipation."@en
doi I D ap W I A S. P R E P R I N T.3082 ep

Electrophysiological Muscle Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrophysiological_Muscle_Model

mathematical model of the neuromuscular system combining continuum mechanics models with electrophysiological models
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
doi I D ap gamm.202370009 ep

Electrophysiological Muscle ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrophysiological_Muscle_Model_ODE_System

three-dimensional electrophysiological model for a muscle
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Electrophysiological Muscle Model ni
contains formulation op Lumped Activation Parameter ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Material Density ni
contains quantity op Material Point Acceleration ni
contains quantity op Material Point Velocity ni
contains quantity op Pressure ni
contains quantity op Stress Tensor (Piola-Kirchhoff) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \rho_{\text{M}1} \mathbf{\ddot{x}}_{\text{M}1} &= \mathbf{\nabla} \cdot \left(\mathbf{P}_{\text{passive}}(\mathbf{F}_{\text{M}1}) + \mathbf{P}_{\text{active}}(\mathbf{F}_{\text{M}1}, \gamma_{\text{M}1}) - p_{\text{M}1}\mathbf{F}^{-T}_{\text{M}1} \right), &\text{div $\mathbf{\dot{x}}_{\text{M}1} = 0$} ~ &\text{in $\Omega_{\text{M}1}\times [0,T_{\text{end}})$}\\ \rho_{\text{M}2} \mathbf{\ddot{x}}_{\text{M}2} &= \mathbf{\nabla} \cdot \left(\mathbf{P}_{\text{passive}}(\mathbf{F}_{\text{M}2}) + \mathbf{P}_{\text{active}}(\mathbf{F}_{\text{M}2}, \gamma_{\text{M}2}) - p_{\text{M}2}\mathbf{F}^{-T}_{\text{M}2} \right), &\text{div $\mathbf{\dot{x}}_{\text{M}2} = 0$} ~ &\text{in $\Omega_{\text{M}2}\times [0,T_{\text{end}})$}\\ \rho_{\text{T}}\mathbf{\ddot{x}}_\text{T}&= \mathbf{\nabla} \cdot \left(\mathbf{P}_\text{passive}(\mathbf{F}_{\text{T}}) - p_\text{T}\mathbf{F}^{-T}_{\text{T}}\right), &\text{div $\mathbf{\dot{x}}_{\text{T}}=0$}& ~\text{in $\Omega_{\text{T}}\times [0,T_{\text{end}})$} \end{align}$"^^La Te X ep
in defining formulation dp "$\ddot{\mathbf{x}}$, Material Point Acceleration"^^La Te X ep
in defining formulation dp "$\dot{\mathbf{x}}$, Material Point Velocity"^^La Te X ep
in defining formulation dp "$\gamma$, Lumped Activation Parameter"^^La Te X ep
in defining formulation dp "$\mathbf{P}$, Stress Tensor (Piola-Kirchhoff)"^^La Te X ep
in defining formulation dp "$\mathbf{x}$, Displacement Muscle Tendon"^^La Te X ep
in defining formulation dp "$\rho$, Material Density"^^La Te X ep
in defining formulation dp "$p$, Pressure"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "One continuum mechanics three-dimensional model for each participant. The equations originate from conservation of mass and momentum for each participant."@en

Elementary Chargeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElementaryCharge

electric charge carried by a single proton or a single positron
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by op Electric Charge ni
qudt I D ap Elementary Charge ep
wikidata I D ap Q2101 ep

Empirical Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EmpiricalDistributionOfIndividuals

empirical distribution of individuals that follow a specific medium and influencer
belongs to
Quantity c
has facts
description ap "Empirical distribution of individuals that follow a specific medium and influencer at a given time by the sum of Dirac Delta distributions placed at the individuals’ opinions."@en

Empirical Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EmpiricalDistributionOfIndividualsFormulation

empirical distribution of individuals that follow a medium and influencer
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Dirac Delta Distribution ni
contains quantity op Empirical Distribution Of Individuals ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Medium Follower Matrix ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Total Number Of Individuals ni
defining formulation dp "$\rho_{m, l}^{(N)}(x, t)=\frac{1}{N} \sum_{\substack{i: B_{i m}=1 \\ C_{i l}(t)=1}} \delta\left(x-x_i(t)\right)$"^^La Te X ep
in defining formulation dp "$B_im$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$C_im$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$N$, Total Number Of Individuals"^^La Te X ep
in defining formulation dp "$\delta$, Dirac Delta Distribution"^^La Te X ep
in defining formulation dp "$\rho_{m, l}^{(N)}$, Empirical Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
in defining formulation dp "$x_i$, Opinion"^^La Te X ep
is dimensionless dp "true"^^boolean
description ap "Empirical distribution of individuals that follow a medium m and influencer l at time t by the sum of Dirac Delta distributions $\delta$ placed at the individuals’ opinions. This distribution describes the stochastic opinion instances at a given time and integrates to $\int_D \rho_{m, l}^{(N)}(x, t) d x=: n_{m, l}^{(N)}(t)$, the proportion of individuals that follow medium m and influencer l."@en

Energyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Energy

quantitative property of a physical system, recognizable in the performance of work and in the form of heat and light
belongs to
Quantity Kind c
has facts
qudt I D ap Energy ep
wikidata I D ap Q11379 ep

Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1ComplexConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_1}}{dt} = k_{4} c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-5} c_{E} c_{P_1} - k_{-4} c_{EP_1} c_{P_2} - k_{5} c_{EP_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1ComplexConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_1}}{dt} = k_{4} c_{EP_{1}P_{2}} + k_{-5} c_{E} c_{P_1} - k_{-4} c_{EP_1} c_{P_2} - k_{5} c_{EP_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1-Product2ComplexConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_{1}P_{2}}}{dt} = k_{3} c_{ES_{1}S_{2}} + k_{-4} c_{EP_1} c_{P_2} - k_{-3} c_{EP_{1}P_{2}} - k_{4} c_{EP_{1}P_{2}}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}P_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Product 1 - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct1Product2ComplexConcentration

amount of enzyme - product 1 - product 2 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme - Product 1 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct1ComplexConcentration

amount of enzyme - product 1 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product2ComplexConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_2}}{dt} = k_{2} c_{ES_1} c_{S_2} + k_{-3} c_{E} c_{P_2} - k_{-2} c_{EP_2} c_{P_1} - k_3 c_{EP_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct2ComplexConcentration

amount of enzyme - product 2 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrateComplexConcentrationODEUniUni

ordinary differential equation describing the concentration over time in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES}}{dt}=k_{1}*c_{E}*c_{S}-k_{-1}*c_{ES}-k_{2}*c_{ES}+k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} c_{E} c_{S_1} + k_{-2} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} c_{E} c_{S_1} + k_{-2} c_{ES_{1}S_{2}} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} c_{E} c_{S_1} + k_{-2} c_{E*} c_{P_1} - k_{-1} c_{ES_1} - k_{2} c_{ES_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} c_{E} c_{S_1} + k_{-2} c_{EP_{2}} c_{P_1} - k_{-1} c_{ES_1} - k_2 c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1-Substrate2ComplexConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_{1}S_{2}}}{dt} = k_{2} c_{ES_1} c_{S_2} + k_{-3} c_{EP_{1}P_{2}} - k_{-2} c_{ES_{1}S_{2}} - k_{3} c_{ES_{1}S_{2}}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1-Substrate2Enzyme-Product1-Product2-ComplexConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_{1}E_{2}=EP_{1}P_{2}}}{dt} = k_2 c_{ES_1} c_{S_2} - k_{-2} c_{ES_{1}E_{2}=EP_{1}P_{2}} - k_4 c_{ES_{1}E_{2}=EP_{1}P_{2}} + k_{-4} c_{EP_1} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1Substrate2EnzymeProduct1Product2ComplexConcentration

amount of enzyme - substrate 1 - substrate 2 = enzyme -product 1 - product 2 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme - Substrate 1 - Substrate 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1Substrate2ComplexConcentration

amount of enzyme - substrate 1 - substrate 2 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme - Substrate 1 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1ComplexConcentration

amount of enzyme - substrate 1 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentration

amount of enzyme present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} c_{ES_1} + k_5 c_{EP_1} - k_{1} c_{E} c_{S_1} - k_{-5} c_{E} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} c_{ES_1} + k_5 c_{EP_1} - k_{1} c_{E} c_{S_1} - k_{-5} c_{E} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} c_{ES_1} + k_{4} c_{E*S_2} - k_{1} c_{E} c_{S_1} - k_{-4} c_{E} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} c_{ES_1} + k_3 c_{EP_2} - k_{1} c_{E} c_{S_1} - k_{-3} c_{E} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEUniUni

ordinary differential equation describing the concentration over time in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt}=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}+k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme Conservationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzmeConservation

enzyme molecules are neither formed nor destroyed during the reaction
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Enzyme Concentration ni
defining formulation dp "$c_{E_{0}} = c_{E} + c_{EX}$"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep

Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeKinetics

study of rates of enzyme-catalyzed reactions
belongs to
Research Field c
has facts
contains problem op Bi Bi Reaction ni
wikidata I D ap Q883112 ep

Enzyme-Substrate Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrateComplexConcentration

amount of enzyme-substrate complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Complexed Enzyme Concentration ni
generalized by quantity op Concentration ni

Epidemiologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Epidemiology

study of the patterns, causes, and effects of health and disease conditions
belongs to
Research Field c
has facts
wikidata I D ap Q133805 ep

Equilibrium Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstant

equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached after sufficient time
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q857809 ep

Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSingleCCSS

equilibrium constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_1 k_2 k_4 k_5}{k_{-1} k_{-2} k_{-4} k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSS

equilibrium constant of bi bi rection following ordered mechnism with steady state assumption
belongs to
Quantity c
has facts
defined by op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition) ni
generalized by quantity op Equilibrium Constant ni
is dimensionless dp "true"^^boolean

Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSSDefinition

equilibrium constant of bi bi rection following ordered mechnism with steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} \equiv \frac{k_1 k_2 k_3 k_4 k_5}{k_{-1} k_{-2} k_{-3} k_{-4} k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionPingPongSS

equilibrium constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_{1} k_{2} k_{3} k_{4}}{k_{-1} k_{-2} k_{-3} k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionTheorellChanceSS

equilibrium constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_1 k_2 k_3}{k_{-1} k_{-2} k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Ermoneit (2023) Optimal control of conveyor-mode spin-qubit shuttling in a Si/SiGe quantum bus in the presence of charged defectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Ermoneit_2023_Optimal_control_of_conveyor-mode_spin-qubit_shuttling_in_a_Si_SiGe_quantum_bus_in_the_presence_of_charged_defects

publication
belongs to
Publication c
has facts
doi I D ap W I A S. P R E P R I N T.3082 ep

Euler Backward Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerBackwardMethod

In numerical analysis and scientific computing, this method is one of the most basic numerical methods for the solution of ordinary differential equations
belongs to
Mathematical Formulation c
has facts
contains quantity op Time Step ni
generalizes formulation op Darcy Equation (Euler Backward) ni
generalizes formulation op Stokes Equation (Euler Backward) ni
defining formulation dp "$y_{n+1}=y_{n}+h f\left(t_{n+1}, y_{n+1}\right)$"^^La Te X ep
in defining formulation dp "$f$, function occuring on the right-hand-side of the ODE or PDE under consideration"^^La Te X ep
in defining formulation dp "$h$, Time Step"^^La Te X ep
in defining formulation dp "$h$, size of time step"^^La Te X ep
in defining formulation dp "$n$, index of time step"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, function solving the ODE or PDE under consideration"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "similar to the (standard, forward, explicit) Euler method, but differs in that it is an implicit method. The backward Euler method has error of order one in time."@en
alt Label ap "Implicit Euler Method"
wikidata I D ap Q2736820 ep

Euler Forward Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerForwardMethod

In mathematics and computational science, this method is a first-order numerical procedure for solving ODEs with a given initial value
belongs to
Mathematical Formulation c
has facts
contains quantity op Time ni
contains quantity op Time Step ni
defining formulation dp "$y_{n+1}=y_{n}+h f(t_n, y_n)$"^^La Te X ep
in defining formulation dp "$h$, Time Step"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method."@en
alt Label ap "Forward Euler Method"@en
wikidata I D ap Q868454 ep

Euler Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerNumber

mathematical constant; limit of (1 + 1/n)^n as n approaches infinity
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
description ap "transcendental number approximately equal 2.718281828...."@en
wikidata I D ap Q82435 ep

Excess Substrate Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExcessSubstrateAssumption

substrate concentration much higher than enzyme concentration
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains quantity op Enzyme Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$c_S >> c_E \rightarrow c_S \approx c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{S_{0}}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Substrate Concentration"^^La Te X ep

Excitation Errorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExcitationError

in dynamical electron scattering, the excitation error shows how well the Laue condition is satisfied
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
doi I D ap s11082 020 02356 y ep

Expectation Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValue

long-run average value of a random variable
belongs to
Quantity Kind c
has facts
generalizes quantity op Expectation Value (Quantum Density) ni
wikidata I D ap Q200125 ep

Expectation Value (Quantum Density)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumDensity

expected (mean) value of a quantum-mechanical observable, calculated from a density
belongs to
Quantity c
has facts
defined by op Expectation Value (Quantum Density, Definition) ni
generalizes quantity op Expectation Value (Quantum State) ni
wikidata I D ap Q2918589 ep

Expectation Value (Quantum Density, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumDensityDefinition

expected (mean) value of a quantum-mechanical observable, calculated from a density
belongs to
Mathematical Formulation c
has facts
contains quantity op Expectation Value (Quantum Density) ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Mechanical Operator ni
defining formulation dp "$\langle \hat{O} \rangle \equiv \mathrm{tr}(\hat{O}\hat{\rho})$"^^La Te X ep
in defining formulation dp "$\hat{O}$, Quantum Mechanical Operator"^^La Te X ep
in defining formulation dp "$\langle \hat{O} \rangle$, Expectation Value (Quantum Density)"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
wikidata I D ap Q2918589 ep

Expectation Value (Quantum State)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumState

expected (mean) value of a quantum-mechanical observable, calculated from a state vector
belongs to
Quantity c
has facts
defined by op Expectation Value (Quantum State, Definition) ni

Expectation Value (Quantum State, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumStateDefinition

expected (mean) value of a quantum-mechanical observable, calculated from a state vector
belongs to
Mathematical Formulation c
has facts
contains quantity op Expectation Value (Quantum State) ni
contains quantity op Quantum Mechanical Operator ni
contains quantity op Quantum State Vector ni
defining formulation dp "$\langle \hat{O} \rangle \equiv \langle \psi |\hat{O}| \psi \rangle$"^^La Te X ep
in defining formulation dp "$\hat{O}$, Quantum Mechanical Operator"^^La Te X ep
in defining formulation dp "$\langle \hat{O} \rangle$, Expectation Value (Quantum State)"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep

Exposure Of An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExposureOfAnIndividual

exposure (time) of an individual at a certain age
belongs to
Quantity c
has facts
generalized by quantity op Time ni

External Chemical Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExternalChemicalPotential

chemical potential on the boundary of a domain, i.e., an interface
belongs to
Quantity c

External Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExternalForceDensity

vector field representing the flux density of the hydrostatic force within the bulk of a fluid
belongs to
Quantity c
has facts
description ap "In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid."@en
wikidata I D ap Q4117184 ep

Extract Logical Rulesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExtractLogicalRules

extract logical rules underlying a boolean ring
belongs to
Computational Task c
has facts
applies model op Object Comparison Model ni
contains formulation op Logical Rule Extraction Formulation ni
contains input op Boolean Ring ni
contains output op Gröbner Basis ni

Extrinsic Mortalityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExtrinsicMortality

sum of the effects of external factors that contribute to death
belongs to
Quantity c
has facts
wikidata I D ap Q60776128 ep

Far Field Radiationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FarFieldRadiation

electromagnetic radiation behaviors that predominate at greater distances
belongs to
Computational Task c
has facts
applies model op Maxwell Equations Model ni
description ap "Shalva: Given ρ(r, t) and j(r, t) that are localized in some domain in space, calculate E(r, t) and B(r, t) far from this domain. For instance, calculate the electromagnetic field emitted by an oscillating dipole."@en
description ap "The far field is a region of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Electromagnetic radiation far-field behaviors predominate at greater distances."@en

Faraday Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FaradayLaw

basic law of electromagnetism of magnetic fields inducing a potential difference
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Time ni
defining formulation dp "$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
alt Label ap "Faraday's law of induction"@en
wikidata I D ap Q181465 ep

Feedforward Neural Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Feedforward_Neural_Network

artificial neural network wherein connections between the nodes do not form a cycle
belongs to
Mathematical Model c
has facts
generalized by op Artificial Neural Network ni
wikidata I D ap Q5441227 ep

Fermi Potential For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FermiPotentialForElectrons

for use in semiconductor physics; strictly speaking, a quasi Fermi potential
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Energy ni
wikidata I D ap Q13633683 ep

Fermi Potential For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FermiPotentialForHoles

for use in semiconductor physics; strictly speaking, a quasi Fermi potential
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Energy ni

Fiber Contraction Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FibreContractionVelocity

speed at which muscle fibers change length during a contraction
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni

Fiber Stretchni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FibreStretch

stretch of a fibre, e.g. in a muscle
belongs to
Quantity c
has facts
generalized by quantity op Linear Strain ni

Fick Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FickEquation

mathematical description for transport of mass|particles by diffusion
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
generalized by formulation op Classical Fokker Planck Equation ni
generalized by formulation op Transport Equation ni
defining formulation dp "$F = - \alpha \nabla u$"^^La Te X ep
in defining formulation dp "$F$, Diffusion Flux"^^La Te X ep
in defining formulation dp "$\alpha$, Diffusion Constant"^^La Te X ep
in defining formulation dp "$u$, Concentration"^^La Te X ep
alt Label ap "Fick's law of diffusion"@en
wikidata I D ap Q856634 ep

Finite Volume Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FiniteVolumeMethod

method for representing and evaluating partial differential equations in the form of algebraic equations
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Continuity Equation For Electrons (Finite Volume) ni
generalizes formulation op Continuity Equation For Holes (Finite Volume) ni
generalizes formulation op Darcy Equation (Finite Volume) ni
generalizes formulation op Poisson Equation For The Electric Potential (Finite Volume) ni
generalizes formulation op Stokes Equation (Finite Volume) ni
is space-continuous dp "false"^^boolean
description ap "Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a solution using local data, and construct a global approximation by stitching them together."@en
description ap "In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume."@en
wikidata I D ap Q1401936 ep

Fixed Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FixedCosts

fixed costs for something, independend of e.g. time, length,...
belongs to
Quantity c
has facts
generalized by quantity op Costs ni
wikidata I D ap Q16897780 ep

Flow in Porous Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FlowInPorousMedia

flow of an incompressible fluid through a porous medium
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Darcy Model ni

Fluid Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDensity

measure of the mass per unit volume of a fluid
belongs to
Quantity c
has facts
generalized by quantity op Particle Number Density ni
alt Label ap "Fluid Mass Density"@en
wikidata I D ap Q101961654 ep

Fluid Dynamic Viscosity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDynamicViscosityFreeFlow

physical property of a moving fluid in free flow
belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
wikidata I D ap Q15152757 ep

Fluid Dynamic Viscosity (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDynamicViscosityPorousMedium

physical property of a moving fluid in a porous medium
belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
wikidata I D ap Q15152757 ep

Fluid Intrinsic Permeability (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidIntrinsicPermeabilityPorousMedium

measure of the ability of a porous material to allow fluids to pass through it
belongs to
Quantity c
has facts
alt Label ap "Intrinsic Permeability"@en

Fluid Kinematic Viscosity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidKinematicViscosityFreeFlow

characteristic of a fluid in free flow
belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
wikidata I D ap Q15106259 ep

Fluid Pressure (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidPressureFreeFlow

force exerted by a fluid (either a liquid or a gas) per unit area at any point within it in free flow
belongs to
Quantity c
has facts
generalized by quantity op Pressure ni

Fluid Pressure (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidPressurePorousMedium

force exerted by a fluid (either a liquid or a gas) per unit area at any point within it in porous medium
belongs to
Quantity c
has facts
generalized by quantity op Pressure ni

Fluid Velocity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidVelocityFreeFlow

vector field used to describe the motion of a fluid in a mathematical manner in free flow
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
alt Label ap "Macroscopic Velocity (Free Flow)"@en

Fluid Velocity (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidVelocityPorousMedium

vector field used to describe the motion of a fluid in a mathematical manner in porous medium
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
alt Label ap "Macroscopic Velocity (Porous Medium)"@en

Fluid Viscous Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidViscousStress

models stress in continuum mechanics due to strain rate
belongs to
Quantity c
has facts
description ap "The viscous stress tensor models stress in continuum mechanics due to strain rate, representing material deformation at a point."@en
wikidata I D ap Q7935892 ep

Flux Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluxOfElectrons

flow of electrons, e.g., in an electric device
belongs to
Quantity c
has facts
generalized by quantity op Particle Flux Density ni
description ap "For use in semiconductor physics"@en

Flux Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluxOfHoles

flow of holes, e.g., in an electric device
belongs to
Quantity c
has facts
generalized by quantity op Particle Flux Density ni
description ap "For use in semiconductor physics"@en

Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Force

physical influence that tends to cause an object to change motion unless opposed by other forces
belongs to
Quantity Kind c
has facts
qudt I D ap Force ep
wikidata I D ap Q11402 ep

Force Constant (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceConstantAnharmonic

coefficients of the nth (n>=3) order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration
belongs to
Quantity c
has facts
generalizes quantity op Force Constant (Harmonic) ni
description ap "Cubic, quartic, ... anharmonic force constants are the coefficients of the third, fourth, ... order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration."@en
wikidata I D ap Q545228 ep

Force Constant (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceConstantHarmonic

coefficients of the second order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration
belongs to
Quantity c
is same as
Spring Constant ni
has facts
same As ep Spring Constant ni
wikidata I D ap Q170282 ep

Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceDensity

in fluid mechanics, negative gradient of pressure
belongs to
Quantity c
has facts
generalizes quantity op External Force Density ni
generalizes quantity op Surface Force Density ni
description ap "It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid"@en
wikidata I D ap Q4117184 ep

Fourier Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FourierEquation

differential form of Fourier's law of thermal conduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Temperature ni
generalized by formulation op Transport Equation ni
defining formulation dp "$q = - \gamma \nabla T$"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\gamma$, Thermal Conductivity"^^La Te X ep
in defining formulation dp "$q$, Heat Flux"^^La Te X ep
description ap "Assuming that the local heat flux is equal to the product of thermal conductivity and the negative local temperature gradient"@en
alt Label ap "Fourier's law of heat conduction"@en
wikidata I D ap Q12016821 ep

Fraction Of Population Density Of Exposedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfExposed

fraction of population density of exposed Individuals
belongs to
Quantity c
has facts
generalized by quantity op Population Density ni

Fraction Of Population Density Of Exposed Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfExposedFormulation

equation describing the fraction of population density of exposed individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$e(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_e^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$e(x, 0)$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$w_e^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Fraction Of Population Density Of Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfInfectious

fraction of population density of Infectious Individuals
belongs to
Quantity c
has facts
generalized by quantity op Population Density ni

Fraction Of Population Density Of Infectious Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfInfectiousFormulation

equation describing the fraction of population density of infectious individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$i(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_i^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$i(x, 0)$, Fraction Of Population Density of Infectious"^^La Te X ep
in defining formulation dp "$w_i^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Fraction Of Population Density Of Removedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfRemoved

fraction of population density of removed Individuals
belongs to
Quantity c
has facts
generalized by quantity op Population Density ni

Fraction Of Population Density Of Susceptiblesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfSusceptibles

fraction of population density of susceptible Individuals
belongs to
Quantity c
has facts
generalized by quantity op Population Density ni

Fraction Of Population Density Of Susceptibles Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfSusceptiblesFormulation

equation describing the fraction of population density of susceptible individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$$ s(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_s^{(\tilde{l})} G^{(\tilde{l})}(x)$$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$s(x, 0)$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$w_s^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Free Energy Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeEnergyDensity

measure of the increase in the Helmholtz free energy per unit volume due to distortions
belongs to
Quantity c
has facts
wikidata I D ap Q865821 ep

Free Fall Determine Gravitationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineGravitation

given the time that it takes for an object to freely fall from a certain height to the ground, what is the magnitude of the gravitational acceleration
belongs to
Computational Task c
has facts
applies model op Free Fall Model (Vacuum) ni
contains input op Free Fall Impact Time ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Gravitational Acceleration (Earth Surface) ni

Free Fall Determine Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineTime

how long does it take for a freely falling object to fall to the ground
belongs to
Computational Task c
has facts
applies model op Free Fall Model (Air Drag) ni
applies model op Free Fall Model (Vacuum) ni
contains assumption op Uniform Gravitational Acceleration ni
contains constant op Gravitational Acceleration (Earth Surface) ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Free Fall Impact Time ni

Free Fall Determine Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineVelocity

with which velocity will a freely falling object hit the ground
belongs to
Computational Task c
has facts
applies model op Free Fall Model (Air Drag) ni
applies model op Free Fall Model (Vacuum) ni
contains constant op Gravitational Acceleration (Earth Surface) ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Free Fall Impact Velocity ni

Free Fall Equation (Air Drag)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationAirDrag

modeling the fall of objects by the laws of classical mechanics, including aerodynamic drag and assuming a uniform gravitational field
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Free Fall Model (Air Drag) ni
contains quantity op Cross Section ni
contains quantity op Density Of Air ni
contains quantity op Drag Coefficient ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Mass ni
contains quantity op Free Fall Terminal Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} m\dot{v} &=& mg-\frac{1}{2}\rho C_DAv^2\\ v(t) &=& v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \\ y(t) &=& y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Cross Section"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep
in defining formulation dp "$\rho$, Density of Air"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$m$, Free Fall Mass"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$v_{\infty}$, Free Fall Terminal Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
is linear dp "false"^^boolean
description ap "Moreover, assuming the falling object to be a point mass."@en
wikidata I D ap Q38083707 ep

Free Fall Equation (Non-Uniform Gravitation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationNonUniformGravitation

modeling the fall of objects by the laws of classical mechanics, neglecting aerodynamic drag but allowing for a non-uniform gravitational field
belongs to
Mathematical Formulation c
has facts
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Time ni
contains quantity op Quantile Function Of The Beta Distribution ni
contains quantity op Time ni
generalizes formulation op Free Fall Equation (Vacuum) ni
defining formulation dp "$y(t)=y_0Q\left(1-\frac{t}{t_{\mathrm{ff}}};\frac{3}{2},\frac{1}{2}\right)$"^^La Te X ep
in defining formulation dp "$t$, Time"
in defining formulation dp "$Q$, Quantile Function Of The Beta Distribution"^^La Te X ep
in defining formulation dp "$t_\mathrm{ff}$, Free Fall Time"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "Moreover, assuming the falling object to be a point mass."@en

Free Fall Equation (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationVacuum

modeling the fall of objects by the laws of classical mechanics, neglecting aerodynamic drag and assuming a uniform gravitational field
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Free Fall Model (Vacuum) ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Time ni
generalized by formulation op Free Fall Equation (Air Drag) ni
defining formulation dp "$\begin{align} \dot{v} &=& g \\ v(t) &=& v_0-gt \\ y(t) &=& y_0+v_0t-\frac{1}{2}gt^2 \end{align}$"^^La Te X ep
defining formulation dp "$v(t)=v_0-gt$"^^La Te X ep
defining formulation dp "$y(t)=y_0+v_0t-\frac{1}{2}gt^2$"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "Moreover, assuming the falling object to be a point mass."@en
wikidata I D ap Q38083707 ep

Free Fall Heightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallHeight

height of an object as it falls freely
belongs to
Quantity c
has facts
generalized by quantity op Length ni
alt Label ap "Free Fall Altitude"@en
wikidata I D ap Q140028 ep

Free Fall Impact Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallImpactTime

time that it takes for an object to freely fall from a certain height to the ground
belongs to
Quantity c
has facts
generalized by quantity op Free Fall Time ni
wikidata I D ap Q5499609 ep

Free Fall Impact Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallImpactVelocity

velocity with which a freely falling object hits the ground
belongs to
Quantity c
has facts
generalized by quantity op Classical Velocity ni

Free Fall Initial Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialCondition

initial height and velocity of an object before it falls through a fluid or a gas
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Free Fall Equation (Air Drag) ni
contained as initial condition in op Free Fall Model (Vacuum) ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Time ni
defining formulation dp "\begin{align} y(t=0) &= y_0 \\ v(t=0) &= v_0 \end{align}"^^La Te X ep
in defining formulation dp "$t$, time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep

Free Fall Initial Heightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialHeight

initial height of an object as it starts falling through a fluid or a gas
belongs to
Quantity c
has facts
defined by op Initial Classical Position ni
generalized by quantity op Free Fall Height ni
alt Label ap "Free Fall Initial Altitude"@en

Free Fall Initial Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialVelocity

initial velocity of an object as it starts falling through a fluid or a gas
belongs to
Quantity c
has facts
defined by op Initial Classical Velocity ni
generalized by quantity op Free Fall Velocity ni

Free Fall Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallMass

mass of a (freely) falling object
belongs to
Quantity c
has facts
generalized by quantity op Mass ni

Free Fall Model (Air Drag)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelAirDrag

mathematical model for the fall of objects, including the aerodynamic drag and assuming a uniform gravitational field
belongs to
Mathematical Model c
has facts
models op Gravitational Effects On Fruit ni
wikidata I D ap Q38083707 ep

Free Fall Model (Non-Uniform Gravitation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelNonUniformGravitation

mathematical model for the fall of objects, including the aerodynamic drag and allowing for a non-uniform gravitational field
belongs to
Mathematical Model c
has facts
contains formulation op Free Fall Equation (Non-Uniform Gravitation) ni
contains initial condition op Free Fall Initial Condition ni
generalizes model op Free Fall Model (Vacuum) ni
models op Gravitational Effects On Fruit ni
wikidata I D ap Free fall ep

Free Fall Model (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelVacuum

mathematical model for the fall of objects, neglecting aerodynamic drag and assuming a uniform gravitational field
belongs to
Mathematical Model c
has facts
contains assumption op Uniform Gravitational Acceleration ni
contains assumption op Vanishing Air Density ni
contains assumption op Vanishing Drag Coefficient ni
generalized by model op Free Fall Model (Air Drag) ni
models op Gravitational Effects On Fruit ni
description ap "A free fall is any motion of a body where gravity is the only force acting upon it. Hence, we are neglecting the aerodynamic drag (vanishing drag coefficient and/or density of air) and assuming a uniform gravitational field."@en
doi I D ap 012 ep
doi I D ap 1.3246467 ep
wikidata I D ap Q38083707 ep

Free Fall Terminal Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTerminalVelocity

highest velocity attainable by an object as it falls through a fluid or a gas
belongs to
Quantity c
has facts
defined by op Free Fall Terminal Velocity (Definition) ni
generalized by quantity op Classical Velocity ni
generalized by quantity op Free Fall Velocity ni
wikidata I D ap Q614981 ep

Free Fall Terminal Velocity (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTerminalVelocityDefinition

highest velocity attainable by an object as it falls through a fluid or a gas
belongs to
Mathematical Formulation c
has facts
contains quantity op Cross Section ni
contains quantity op Density Of Air ni
contains quantity op Drag Coefficient ni
contains quantity op Free Fall Terminal Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Mass ni
defining formulation dp "$v_\infty \equiv \sqrt{\frac{2mg}{\rho C_D A}}$"^^La Te X ep
in defining formulation dp "$A$, Cross Section"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep
in defining formulation dp "$\rho$, Density Of Air"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$v_\infty$, Free Fall Terminal Velocity"^^La Te X ep
wikidata I D ap Q614981 ep

Free Fall Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTime

characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse
belongs to
Quantity c
has facts
generalized by quantity op Time ni
wikidata I D ap Q5499609 ep

Free Fall Time (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTimeDefinition

characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse
belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Mass ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Mass ni
contains quantity op Free Fall Time ni
contains quantity op Gravitational Constant ni
defines op Free Fall Time ni
defining formulation dp "$t(y) \equiv \sqrt{ \frac{ {y_0}^3 }{2G(m+M)} } \left(\sqrt{\frac{y}{y_0}\left(1-\frac{y}{y_0}\right)} + \arccos{\sqrt{\frac{y}{y_0}}}\right)$"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$M$, Earth Mass"^^La Te X ep
in defining formulation dp "$m$, Free Fall Mass"^^La Te X ep
in defining formulation dp "$t$, Free Fall Time"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
wikidata I D ap Q5499609 ep

Free Fall Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallVelocity

velocity attained by an object as it falls freely
belongs to
Quantity c
has facts
generalized by quantity op Classical Velocity ni
generalizes quantity op Free Fall Terminal Velocity ni
wikidata I D ap Q140028 ep

Free Flow Coupled to Porous Media Flowni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFlowCoupledToPorousMediaFlow

coupled systems of free flow of an incompressible fluid adjacent to a permeable media
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Stokes Darcy Model ni

Free Flow of an Incompressible Fluidni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFlowIncompressibleFluid

free flow of an incompressible fluid (e.g. gas or liquid)
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Stokes Model ni

Frequencyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Frequency

number of occurrences or cycles per time
belongs to
Quantity Kind c
has facts
qudt I D ap Frequency ep
wikidata I D ap Q11652 ep

Friction Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FrictionCoefficient

measure that quantifies the amount of friction existing between two surfaces
belongs to
Quantity c
has facts
description ap "coefficient of friction, aka damping constant. Units of inverse time"@en
alt Label ap "Damping Constant"@en
wikidata I D ap Q82580 ep

Gamma-Gompertz-Makeham Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GammaGompertzMakehamModel

mathematical model for the mortality based on a Gamma-Gompertz-Makeham law
belongs to
Mathematical Model c
has facts
description ap "We assume that death counts at age x are Poisson-distributed and the underlying population level hazard function follows a Gamma-Gompertz-Makeham model."@en
wikidata I D ap Q2734378 ep

Gamma-Gompertz–Makeham Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GammaGompertzMakehamLaw

mathematical formulation for the mortality based on a Gamma-Gompertz-Makeham law
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Extrinsic Mortality ni
contains quantity op Heterogeneity of Death Rate ni
contains quantity op Level Of Mortality ni
contains quantity op Rate Of Aging ni
contains quantity op Risk Of Death ni
generalized by formulation op Gompertz–Makeham Law ni
defining formulation dp "$\mu(x) = \frac{a\exp(bx)}{1+\frac{a\gamma}{b}(\exp(bx)-1)}+c$"^^La Te X ep
in defining formulation dp "$\gamma$, Heterogeneity of Death Rate"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$a$, Level of Mortality"^^La Te X ep
in defining formulation dp "$b$, Rate Of Aging"^^La Te X ep
in defining formulation dp "$c$, Extrinsic Mortality"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep
doi I D ap journal.pone.0198485 ep

Gattermann (2017) Line pool generationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Gattermann_2017_Line_pool_generation

publication
belongs to
Publication c
has facts
doi I D ap s12469 016 0127 x ep

Gauss Law (Electric Field)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussLawElectricField

foundational law of electromagnetism stating that electric charges are the "sources" (divergence) of electric fields
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Charge Density ni
contains quantity op Electric Field ni
contains quantity op Permittivity (Vacuum) ni
generalizes formulation op Laplace Equation For The Electric Potential ni
generalizes formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$\nabla\cdot E=\frac{\rho}{\epsilon_0}$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\rho$, Electric Charge Density"^^La Te X ep
wikidata I D ap Q173356 ep

Gauss Law (Magnetic Field)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussLawMagneticField

foundational law of electromagnetism stating that the magnetic field B has divergence equal to zero
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Magnetic Field ni
defining formulation dp "$\nabla\cdot B=0$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
description ap "Equivalently, magnetic monopoles do not exist"@en
wikidata I D ap Q1195250 ep

Gaussian Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianDistribution

continuous probability distribution that is symmetric and bell-shaped
belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
alt Label ap "Normal Distribution"@en

Gaussian Distribution (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianDistributionDefinition

continuous probability distribution that is symmetric and bell-shaped
belongs to
Mathematical Formulation c
has facts
contains quantity op Euler Number ni
contains quantity op Expectation Value ni
contains quantity op Gaussian Distribution ni
contains quantity op Pi Number ni
contains quantity op Variance ni
defines op Gaussian Distribution ni
defining formulation dp "$\varphi(z) \equiv \frac 1 {\sigma\sqrt{2\pi}} e^{ -(z-\mu)^2/(2\sigma^2) }$"^^La Te X ep
in defining formulation dp "$\mu$, Expectation Value"^^La Te X ep
in defining formulation dp "$\pi$, Pi Number"^^La Te X ep
in defining formulation dp "$\sigma$, Variance"^^La Te X ep
in defining formulation dp "$\varphi$, Gaussian Distribution"^^La Te X ep
in defining formulation dp "$e$, Euler Number"^^La Te X ep
wikidata I D ap Q2725903 ep

Gaussian Noise Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianNoiseModel

signal noise that has a probability density function equal to that of the normal distribution
belongs to
Mathematical Model c
has facts
contains formulation op Gaussian Distribution (Definition) ni
description ap "A typical model of image noise is Gaussian, additive, independent at each pixel, and independent of the signal intensity, caused primarily by Johnson–Nyquist noise (thermal noise), including that which comes from the reset noise of capacitors ("kTC noise")."@en
alt Label ap "Electronic Noise Model"@en
wikidata I D ap Q2725903 ep

Gompertz Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GompertzLaw

in probability and statistics, the Gompertz distribution is a continuous probability distribution
belongs to
Mathematical Formulation c
has facts
description ap "Often applied to describe the distribution of adult lifespans by demographers."@en
wikidata I D ap Q1011784 ep

Gompertz–Makeham Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GompertzMakehamLaw

mathematical equation describing the human death rate as a sum of an age-dependent component, and an age-independent component
belongs to
Mathematical Formulation c
has facts
generalized by formulation op Gompertz Law ni
description ap "Note that the age-dependent component increases exponentially with age"@en
wikidata I D ap Q2734378 ep

Gramian Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedControllability

generalized Gramian of controllability, for use in bi-linear control problems
belongs to
Quantity c
has facts
defined by op Gramian Generalized Controllability (Definition) ni
generalized by quantity op Gramian Matrix Observability ni

Gramian Generalized Controllability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedControllabilityDefinition

generalized Gramian of controllability, for use in bi-linear control problems
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Controllability ni
contains quantity op Time ni
defining formulation dp "$\begin{align} W_c &=& \sum_{j=1}^{\infty} \int_0^\infty\ldots\int_0^\infty P_{j}(t_{1},\ldots t_{j}) P^{*}_{j}(t_{1}, \ldots t_{j}) \mathrm{d} t_{1} \ldots \mathrm{d} t_{j} \\ P_{1}(t_{1}) &=& e^{A t_{1}}iB \\ P_{j}(t_{1},\ldots,t_{j}) &=& e^{At_{j}}iN P_{j-1} \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Controllability"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Gramian Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedObservability

generalized Gramian of observability, for use in bi-linear control problems
belongs to
Quantity c
has facts
defined by op Gramian Generalized Observability (Definition) ni
generalized by quantity op Gramian Matrix Observability ni

Gramian Generalized Observability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedObservabilityDefinition

generalized Gramian of observability, for use in bi-linear control problems
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Observability ni
contains quantity op Time ni
defining formulation dp "$\begin{align} W_c &=& \sum_{j=1}^{\infty} \int_0^\infty\ldots\int_0^\infty Q^{*}_{j}(t_{1},\ldots t_{j})Q_{j}(t_{1},\ldots t_{j})\mathrm{d} t_{1}\ldots\mathrm{d} t_{j} \\ Q_{1}(t_{1}) &=& C e^{A^{*} t_{1}} \\ Q_{j}(t_{1},\ldots,t_{j}) X&=& Q_{j-1}iN e^{A^{*}t_{j}} \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Generalized Observability"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Gramian Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrix

matrix of inner products of a set of vectors
belongs to
Quantity c
has facts
generalizes quantity op Gramian Matrix Controllability ni
generalizes quantity op Gramian Matrix Observability ni
wikidata I D ap Q1409400 ep

Gramian Matrix Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixControllability

matrix used in linear control problems to determine whether a system is controllable
belongs to
Quantity c
has facts
contained in formulation op Lyapunov Equation Controllability ni
defined by op Gramian Matrix Controllability (Definition) ni

Gramian Matrix Controllability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixControllabilityDefinition

matrix used in linear control problems to determine whether a system is controllable
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Gramian Matrix Controllability ni
defining formulation dp "$W_c \equiv \int_0^\infty e^{At}iB(-i)B^* e^{A^*t}\mathrm{d} t$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep

Gramian Matrix Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixObservability

matrix used in linear control problems to determine whether a system is observable
belongs to
Quantity c
has facts
contained in formulation op Lyapunov Equation Observability ni
defined by op Gramian Matrix Observability (Definition) ni

Gramian Matrix Observability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixObservabilityDefinition

matrix used in linear control problems to determine whether a system is observable
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Gramian Matrix Observability ni
defining formulation dp "$W_o \equiv \int_0^\infty e^{A^*t}C^*C e^{At}\mathrm{d} t$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep

Graph Type Identifierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GraphTypeIdentifier

variable identifying a graph as directed (value=1) or undirected (value=2)
belongs to
Quantity c
has facts
contained in formulation op Line Costs Computation ni
defined by op Graph Type Identifier (Definition) ni

Graph Type Identifier (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GraphTypeIdentifierDefinition

variable identifying a graph as directed (value=1) or undirected (value=2)
belongs to
Mathematical Formulation c
has facts
contains quantity op Decision Variable ni
defining formulation dp "$x \equiv \left\{ \begin{array}{ll} 1 & \textrm{graph directed}\\ 2 & \textrm{graph undirected} \\ \end{array} \right. $"^^La Te X ep
in defining formulation dp "$x$, Decision Variable"^^La Te X ep

Gravitational Acceleration (Earth Surface)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalAccelerationEarthSurface

acceleration of an object in free fall within a vacuum, thus without experiencing drag
belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni
description ap "At a fixed point on the surface of Earth, the gravity results from the combined effect of gravitation and the centrifugal force from Earth's rotation. At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s2."@en
qudt I D ap Acceleration Of Gravity ep
wikidata I D ap Q30006 ep

Gravitational Acceleration (Earth Surface, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalAccelerationEarthSurfaceDefinition

acceleration of an object in free fall within a vacuum, thus without experiencing drag
belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Mass ni
contains quantity op Earth Radius ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Gravitational Constant ni
defines op Gravitational Acceleration (Earth Surface) ni
defining formulation dp "$\vec{g} \equiv -\frac{GM}{r^2}\vec{r}$"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$M$, Earth Mass"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$r$, Earth Radius"^^La Te X ep
qudt I D ap Standard Acceleration Of Gravity ep
wikidata I D ap Q30006 ep

Gravitational Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalConstant

physical constant relating the gravitational force between objects to their mass and distance
belongs to
Quantity c
has facts
qudt I D ap Gravitational Constant ep
wikidata I D ap Q18373 ep

Gravitational Effects On Fruitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalEffectsOnFruit

studying how fruits are falling from trees, which inspired Newton of gravitation
belongs to
Research Problem c
has facts
contained in field op Classical Mechanics ni
contained in field op Pomology ni
modeled by op Free Fall Model (Vacuum) ni

Gröbner Basisni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GroebnerBasis

particular generating subset of an ideal in a polynomial ring
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q1551631 ep

H2 Optimal Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#H2OptimalApproximation

model order reduction by interpolation of the Volterra series representation of the system's transfer function
belongs to
Computational Task c
has facts
applies model op Control System Model ni
description ap "This approach is based on the interpolation of the Volterra series representation of the system's transfer function and gives a local H2-optimal approximation, because the interpolation is chosen so that the system satisfies the necessary H2-optimality conditions upon convergence of the algorithm. Note that H2 stands for Hardy space"@en
doi I D ap j.cpc.2018.02.022 ep
doi I D ap 110836742 ep
doi I D ap jcd.2020001 ep

Hanes (1932) Studies on plant amylases: The effect of starch concentration upon the velocity of hydrolysis by the amylase of germinated barleyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hanes_1932_Studies_on_plant_amylases_The_effect_of_starch_concentration_upon_the_velocity_of_hydrolysis_by_the_amylase_of_germinated_barley

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Steady State Assumption) ni
doi I D ap bj0261406 ep

Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductSteadyStateAssumption

equation for uni uni reaction without product following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductIrreversibilityAssumption

equation for uni uni reaction without product following irreversibility assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

equation for uni uni reaction without product following rapid equilibrium assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S}{V_{max,f}} + \frac{K_S (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{c_S}{v_0} = \frac{c_S (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_m (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_m (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hankel Singular Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HankelSingularValue

In control theory, a measure of energy for each state in a system
belongs to
Quantity c
has facts
description ap "In control theory, Hankel singular values, named after Hermann Hankel, are the basis for balanced model reduction, in which controllable and observable states are retained while the remaining states are discarded. The reduced model retains the important features of the original model."@en
wikidata I D ap Q5648530 ep

Heat Conduction Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatConductionModel

mathematical model for thermal conduction based on Fourier's law
belongs to
Mathematical Model c
has facts
contains formulation op Fourier Equation ni
models op Heat Transport ni

Heat Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatFlux

heat transferred per area and time
belongs to
Quantity c
has facts
contained in formulation op Fourier Equation ni
alt Label ap "Heat Flux Density"@en
wikidata I D ap Q1478382 ep

Heat Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatTransport

transfer of heat can be classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni

Helfmann (2023) Modelling opinion dynamics under the impact of influencer and media strategiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Helfmann_2023_Modelling_opinion_dynamics_under_the_impact_of_influencer_and_media_strategies

publication
belongs to
Publication c
has facts
documents op Opinion Model With Influencers And Media ni
documents op Partial Mean Field Opinion Model ni
doi I D ap s41598 023 46187 9 ep

Heterogeneity of Death Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeterogeneityOfDeathRate

shows the different level of susceptibility to dying
belongs to
Quantity c

Hill-Type Two-Muscle-One-Tendon Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hill-Type_Two-Muscle-One-Tendon_Model

mathematical model derived from the balancing forces at the muscle ends
belongs to
Mathematical Model c
has facts
models op Muscle Movement ni
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
doi I D ap gamm.202370009 ep
wikidata I D ap Q10331394 ep

Hill-Type Two-Muscle-One-Tendon ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hill-Type_Two-Muscle-One-Tendon_ODE_System

system of ordinary differential equations describing passive and active muscle forces
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Hill-Type Two-Muscle-One-Tendon Model ni
contains quantity op Active Contractile Force ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Effective Mass (Spring-Mass System) ni
contains quantity op Passive Muscle Force ni
contains quantity op Passive Tendon Force ni
contains quantity op Time ni
defining formulation dp "$ \begin{align} m_{1} \ddot{x}_{1} &= F_\text{PTE}(t) -F_{\text{ACE}1}(t) - F_{\text{PME}1}(t) \\ m_{2} \ddot{x}_{2} &= -F_\text{PTE}(t) + F_{\text{ACE}2}(t) - F_{\text{PME}2}(t) \end{align}$"^^La Te X ep
in defining formulation dp "$F_{\text{ACE}}$, Active contractile force"^^La Te X ep
in defining formulation dp "$F_{\text{PME}}$, Passive Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PTE}}$, Passive Tendon Force"^^La Te X ep
in defining formulation dp "$m$, Effective Mass (Spring-Mass System)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Displacement Muscle Tendon"^^La Te X ep
description ap "System of Ordinary Differential Equations describing passive and active muscle forces during movement on a macroscopic scale, derived by balancing the forces on the muscle ends."@en
wikidata I D ap gamm.202370009 ep
wikidata I D ap Q10331394 ep

Hofstee (1959) Non-inverted versus inverted plots in enzyme kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hofstee_1959_Non_inverted_versus_inverted_plots_in_enzyme_kinetics

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni
doi I D ap 1841296b0 ep

Homogeneous Neumann Boundary Conditionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HomogeneousNeumannBoundaryConditions

homogeneous Neumann boundary conditions
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Diffusion Coefficient ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$\nu^T D \nabla s =\nu^T D \nabla e=\nu^T D \nabla i=\nu^T D \nabla r=0$"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient"^^La Te X ep
in defining formulation dp "$\nu$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep

Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle modelsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Homs-Pons_2024_Coupled_simulations_and_parameter_inversion_for_neural_system_and_electrophysiological_muscle_models

publication
belongs to
Publication c
has facts
doi I D ap gamm.202370009 ep

Hooke Law (Linear Elasticity)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HookeLawLinearElasticity

force to extend or compress a spring by distance scales linearly with distance
belongs to
Mathematical Formulation c
has facts
contains quantity op Displacement Of Atoms ni
contains quantity op Elastic Stiffness Tensor ni
contains quantity op Mechanical Strain ni
contains quantity op Mechanical Stress ni
defining formulation dp "$\sigma=C:\epsilon$ where $\epsilon(u)=\frac{1}{2}(\nabla u+(\nabla u)^T)$"^^La Te X ep
in defining formulation dp "$C$, Elastic Stiffness Tensor"^^La Te X ep
in defining formulation dp "$\epsilon$, Mechanical Strain"^^La Te X ep
in defining formulation dp "$\sigma$, Mechanical Stress"^^La Te X ep
in defining formulation dp "$u$, Displacement of Atoms"^^La Te X ep
description ap "An empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, $F = kx$. Also the stresses and strains of material inside a continuous elastic material are connected by a linear relationship that is mathematically similar to Hooke's spring law, and is often referred to by that name."@en
wikidata I D ap Q1913277 ep
wikidata I D ap Q170282 ep

Hooke Law (Spring)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HookLawSpring

force to extend or compress a spring by distance scales linearly with distance
belongs to
Mathematical Formulation c
has facts
contains quantity op Change In Length ni
contains quantity op Force ni
contains quantity op Spring Constant ni
generalized by formulation op Hooke Law (Linear Elasticity) ni
defining formulation dp "$F = k \Delta l$"^^La Te X ep
in defining formulation dp "$F$, Force"^^La Te X ep
in defining formulation dp "$\Delta l$, Change In Length"^^La Te X ep
in defining formulation dp "$k$, Spring Constant"^^La Te X ep
description ap "An empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, $F = kx$, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke."@en
wikidata I D ap Q170282 ep

Hydraulic Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HydraulicConductivity

measure of the ability of a porous material to allow water to pass through it
belongs to
Quantity c
has facts
wikidata I D ap Q2783041 ep

Hyperstress Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HyperstressPotential

Hyperstress potential in calculations of elasticity
belongs to
Quantity c

Idealni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Ideal

additive subgroup of a ring closed under multiplication by an arbitrary ring element
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q44649 ep

Identify Destruction Rules in Ancient Egyptian Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IdentifyDestructionRulesInAncientEgyptianObjects

identification of rules or patterns of destruction
belongs to
Research Problem c
has facts
contained in field op Egyptology ni
description ap "common destruction patterns in ancient egyptian objects from the 'Cachette de Karnak' suggest that specific rules govern these occurences"@en

Image Denoisingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ImageDenoising

removal of noise from images
belongs to
Research Problem c
has facts
contained in field op Medical Imaging ni
contained in field op Statistics ni
modeled by op Gaussian Noise Model ni
wikidata I D ap Q108033749 ep

Imaging of Nanostructuresni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ImagingOfNanostructures

mathematical model for transmission electron microscopy of nanostructures
belongs to
Research Problem c
has facts
contained in field op Transmission Electron Microscopy ni
modeled by op Dynamical Electron Scattering Model ni
description ap "We present a mathematical model and a tool chain for the numerical simulation of transmission electron microscopy (TEM) images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin–Howie–Whelan equations, describing the propagation of the electron wave through the sample. This tool chain can be applied to generate a database of simulated transmission electron microscopy (TEM) images, which is a key element of a novel concept for model-based geometry reconstruction of semiconductor QDs, involving machine learning techniques."@en
doi I D ap s11082 020 02356 y ep
wikidata I D ap Q110779037 ep

Individual Relationship Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IndividualRelationshipMatrix

relations among individuals such as friendship or connections on social media are defined through a binary adjacency matrix
belongs to
Quantity c
has facts
generalized by quantity op Adjacency Matrix ni

Inertia Parameter For Opinion Changes Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfluencerInertiaParameter

parameter indicating resistance to rapid optinion change of influencers
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni

Inertia Parameter For Opinion Changes Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediaInertiaParameter

parameter indicating resistance to rapid optinion change of media agents
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni

Infected Recovery Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectedRecoveryRate

constant representing the infected recovery rate
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Infectious

general quantity for the number of infectious entities
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
generalizes quantity op Number Of Infectious Individuals ni
generalizes quantity op Number Of Infected Cities ni
is dimensionless dp "true"^^boolean

Infectious At Time Step n+1 in the Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSIModel

equation to define the number of infectious individuals in the multi-population SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}^i = I_n^i + S_n^i \sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSIRModel

equation to define the number of infectious individuals in the multi-population SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}^i = I_n^i \left(1 - \gamma_i \Delta t \right) +S_n^i \sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSISModel

equation to define the number of infectious individuals in the multi-population SIS Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^K \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right) + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIModel

equation to define the number of infectious individuals in the SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1+\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIRModel

equation to define the number of infectious individuals in the SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
discretizes op Continuous Rate of Change of Infectious in the SIR Model ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIRModelWithBirthsAndDeaths

equation to define the number of infectious individuals in the SIR Model with births and deaths
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t - \beta \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#infectiousAtTimeStepInTheSISModel

equation to define the number of infectious individuals in the SIS Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in The SIS Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSISModelWithBirthsAndDEaths

equation to define the number of infectious individuals in the SIS Model with births and deaths
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n + \beta \Delta t (N - S_n)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Influencer Individual Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfluencerIndividualMatrix

adjacency matrix defining the connections between individuals and influencers at time t
belongs to
Quantity c
has facts
generalized by quantity op Adjacency Matrix ni

Inhibition Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstant

chemical constant
belongs to
Quantity c
has facts
generalized by quantity op Dissociation Constant ni

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSingleCCSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_5}{k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSteadyStateAssumption

inhibition constant
belongs to
Quantity c
has facts
defined by op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "Inhibition constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption"@en

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSteadyStateAssumptionDefinition

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} \equiv \frac{k_5}{k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionPingPongSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_{2}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionTheorellChanceSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_{3}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSingleCCSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_4 + k_5}{k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSteadyStateAssumption

inhibition constant
belongs to
Quantity c
has facts
defined by op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "Inhibition constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption"@en

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSteadyStateAssumptionDefinition

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} \equiv \frac{k_4 k_5 + k_3 k_4 + k_3 k_5 + k_{-3} k_5}{k_{-4} (k_3 + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionPingPongSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_{4}}{k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionTheorellChanceSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_{3}}{k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSingleCCSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSteadyStateAssumption

inhibition constant
belongs to
Quantity c
has facts
defined by op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "Inhibition constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption"@en

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSteadyStateAssumptionDefinition

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} \equiv \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionPingPongSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionTheorellChanceSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSingleCCSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-1} + k_{-2}}{k_2}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSteadyStateAssumption

inhibition constant
belongs to
Quantity c
has facts
defined by op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "Inhibition constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption"@en

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSteadyStateAssumptionDefinition

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} \equiv \frac{k_{-1} k_{-2} + k_{-1} k_3 + k_{-1} k_{-3} + k_{-2} k_{-3}}{k_2 (k_3 + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionPingPongSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-3}}{k_{3}}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionTheorellChanceSS

inhibition constant
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-1}}{k_{2}}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibitor Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitorConcentration

amount of inhibitor present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean

Initial Classical Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalDensity

initial phase-space density distribution of a classical mechanical system
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Classical Dynamics Model ni
contains quantity op Classical Density (Phase Space) ni
contains quantity op Time ni
generalized by formulation op Initial Quantum Density ni
defining formulation dp "$\rho(t=0)=\rho_0$"^^La Te X ep
in defining formulation dp "$\rho$, Classical Density (Phase Space)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Classical Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalMomentum

initial momentum of a classical particle modeled as point mass
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Time ni
defining formulation dp "$p(t=0)=p_0$"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Classical Positionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalPosition

initial position of a classical particle modeled as point mass
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Position ni
contains quantity op Time ni
defining formulation dp "$q(t=0)=q_0$"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Classical Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalVelocity

initial velocity of a classical particle modeled as point mass
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Time ni
defining formulation dp "$v(t=0)=v_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep

Initial Condition for the Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSIModel

initial number of susceptible and infectious individuals is equal to the total population of each subdomain
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_0^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0^i$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSISModel

initial number of susceptible and infectious individuals is equal to the total population of each subdomain
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_0^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0^i$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Continuous SI Model and SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheContinuousSIModelAndSISModel

initial number of susceptible and infectious individuals is equal to the total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Continuous Susceptible Infectious Model ni
contained as initial condition in op Continuous Susceptible Infectious Susceptible Model ni
contained as initial condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
discretized by formulation op Initial Condition for the Discrete SI Model ni
defining formulation dp "$S(0) + I(0) = N$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean

Initial Condition for the Continuous SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheContinuousSIRModel

initial number of susceptible, infectious and removed individuals is equal to the total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S(0) + I(0) + R(0) = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_0$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean

Initial Condition for the Discrete SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheDiscreteSIModel

initial number of susceptible and infectious individuals is equal to the total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0 + I_0 = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition For The Discrete SIR Model with and without Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheDiscreteSIRModel

initial number of susceptible, infectious and removed individuals is equal to the total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Discrete Susceptible Infectious Removed Model ni
contained as initial condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
discretizes op Initial Condition for the Continuous SIR Model ni
defining formulation dp "$S_0 + I_0 + R_0 = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_0$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSIRModel

initial number of susceptible, infectious and removed individuals is equal to the total population of each subdomain
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i + R_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Control Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlState

initial state of a control system
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Control System Model (Linear) ni
contains quantity op Control System Initial ni
contains quantity op Control System State ni
contains quantity op Time ni
defines op Control System Initial ni
defining formulation dp "$x(t=0)=x_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$x_0$, Control System Initial"^^La Te X ep

Initial Control State (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlStateReduced

initial state of a control system; after model order reduction
belongs to
Quantity c
has facts
contained as input in op Balanced Truncation (Bi-linear) ni
contained as input in op Balanced Truncation (Linear) ni
contained as input in op H2 Optimal Approximation (Bi-linear) ni
contained as input in op H2 Optimal Approximation (Linear) ni
defined by op Initial Control State (Reduced, Definition) ni

Initial Control State (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlStateReducedDefinition

initial state of a control system; after model order reduction
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System State (Reduced) ni
contains quantity op Initial Control State (Reduced) ni
contains quantity op Time ni
defines op Initial Control State (Reduced) ni
defining formulation dp "$\tilde{x}(t=0) \equiv \tilde{x}_0$"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}_0$, Initial Control State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct1ComplexConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{EP_1}(t=0) = c_{{EP_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct1Product2ComplexConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{EP_{1}P_{2}}(t=0) = c_{{EP_{1}P_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{PS_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct2ComplexConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{EP_2}(t=0) = c_{{EP_2}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrateComplexConcentrationUniUniODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme-Substrate Complex Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES}(t=0) = c_{{ES}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES}$, Enzyme-Substrate Complex Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1Substrate2ComplexConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_{1}S_{2}}(t=0) = c_{{ES_{1}S_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1Substrate2EnzymeProduct1Product2ComplexConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}(t=0) = c_{{ES_{1}S_{2}=EP_{1}P_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiOrderedMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiPingPongMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiTheorellChanceMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationUniUniMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationUniUniODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Inhibitor Concentration (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialInhibitorConcentrationUniUni

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Time ni
defining formulation dp "$c_I(t=0) = c_{I_{0}}$"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialIntermediateSubstrate2ComplexConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{E*S_2}(t=0) = c_{E*S_{2_{0}}}$"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialIntermediateConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E*(t=0) = c_{E*_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Number Of Infected Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialNumberOfInfectedCities

initial number of infected cities
belongs to
Mathematical Formulation c
has facts
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Time ni
defining formulation dp "$(i_m(t=0))_{m=1}^{N_R} = i(0)$"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$i_m(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedwithProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedwithoutProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Product Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiwithProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiwithoutProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChancewithProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChancewithoutProduct1MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedwithProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedwithoutProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiwithProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiwithoutProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChancewithProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChancewithoutProduct2MichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Product Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P}(t=0) = c_{P_{0}}$"^^La Te X ep
in defining formulation dp "$c_{P}$, Product Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction with Product)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniwithProduct

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P}(t=0) = c_{P_0}$"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction without Product)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniwithoutProduct

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Product Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P}$, Product Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Quantum Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialQuantumDensity

initial density matrix of a quantum-mechanical system
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Density Operator ni
contains quantity op Time ni
generalizes formulation op Initial Quantum State ni
defining formulation dp "$\rho(t=0)=\rho_0$"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Quantum Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialQuantumState

initial state vector of a quantum-mechanical system
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum State Vector ni
contains quantity op Time ni
defining formulation dp "$\psi(t=0)=\psi_0$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Reaction Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRate

instantaneous rate at the start of the reaction
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct1

initial rate of ordered bi bi reaction with product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct1andSingleCC

initial rate of ordered bi bi reaction with product 1 and single central complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct2

initial rate of ordered bi bi reaction with product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct2andSingleCC

initial rate of ordered bi bi reaction with product 2 and single central complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProducts1and2

initial rate of ordered bi bi reaction with products 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProducts1and2andSingleCC

initial rate of ordered bi bi reaction with products 1 and 2 and single central complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithoutProducts

initial rate of ordered bi bi reaction without products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithoutProductsandSingleCC

initial rate of ordered bi bi reaction without products and single central complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProduct1

initial rate of ping pong bi bi reaction with product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
similar to problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProduct2

initial rate of ping pong bi bi reaction with product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
similar to problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProducts1and2

initial rate of ping pong bi bi reaction with products 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithoutProducts

initial rate of ping pong bi bi reaction without products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProduct1

initial rate of Theorell-Chance bi bi reaction with product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProducts1and2

initial rate of Theorell-Chance bi bi reaction with products 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProduct2

initial rate of Theorell-Chance bi bi reaction with product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithoutProducts

initial rate of Theorell-Chance bi bi reaction without products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Uni Uni Reaction with Productni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateOfUniUniReactionWithProduct

initial rate of uni uni reaction with product
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product ni
modeled by op Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni

Initial Reaction Rate of Uni Uni Reaction without Productni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateUniUniReactionWithoutProduct

initial rate of uni uni reaction without product
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni

Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandCompetitiveCompleteInhibition

initial rate of uni uni reaction without product and competitive complete inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandCompetitivePartialInhibition

initial rate of uni uni reaction without product and competitive partial inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandMixedCompleteInhibition

initial rate of uni uni reaction without product and mixed complete inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandMixedPartialInhibition

initial rate of uni uni reaction without product and mixed partial inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandNonCompetitiveCompleteInhibition

initial rate of uni uni reaction without product and non-competitive complete inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandNonCompetitivePartialInhibition

initial rate of uni uni reaction without product and non-competitive partial inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandUncompetitiveCompleteInhibition

initial rate of uni uni reaction without product and uncompetitive complete inhibition
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandUncompetitivePartialInhibition

initial rate of uni uni reaction without product and uncompetitive partial inhibition
belongs to
Research Problem c

Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiOrderedMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiTheorellChanceMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiOrderedMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiOrderedODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiPingPongODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiTheorellChanceMichaelisMentenModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiTheorellChanceODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrateConcentrationUniUniODEModel

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Substrate Concentration ni
contains quantity op Time ni
defining formulation dp "$c_S(t=0) = c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate Concentration (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrateConcentrationUniUni

initial concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Substrate Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_S(t=0) = c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Value For Electron Scatteringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialValueForElectronScattering

initial value for electron scattering, used for modeling of transmission electron microscopy
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Dynamical Electron Scattering Model ni
contains quantity op Amplitude Of Electron Wave ni
contains quantity op Reciprocal Lattice ni
contains quantity op Reciprocal Lattice Vectors ni
defining formulation dp "$\varphi_{\mathbf{g}}(0) =\delta_{\mathbf{0},\mathbf{g}} \quad \text{for } \mathbf{g}\in \Lambda_m^*$"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\varphi_{\mathbf{g}}(0)$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep

Integer Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegerDimensionless

number that can be written without a fractional or decimal component
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
description ap "Ακέραιος αριθμός"@el
wikidata I D ap Q12503 ep

Integral Of The Population Density Fraction Of Exposed (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfExposedInitialCondition

integral of the population density fraction of exposed initial condition
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Total Population Density ni
defining formulation dp "$\int_{\Omega^{(l)}} e(x, 0) n(x) d x=\Sigma_{\mathcal{E}} \hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$e(x, 0)$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Integral Of The Population Density Fraction Of Infectious (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfInfectiousInitialCondition

integral of the population density fraction of infectious initial condition
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Total Population Density ni
defining formulation dp "$\int_{\Omega^{(l)}} i(x, 0) n(x) d x=\hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$i(x, 0)$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Integral Of The Population Density Fraction Of Susceptibles (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfSusceptiblesInitialCondition

integral of the population density fraction of susceptibles initial condition
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Total Population Density ni
contains quantity op Total Population Size ni
defining formulation dp "$ \int_{\Omega^{(l)}} s(x, 0) n(x) dx = \hat{\mathcal{N}}_l-\left(1+\Sigma_{\mathcal{E}}\right) \hat{\mathcal{I}}^{(l)}-\hat{\mathcal{R}}^{(l)} $"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{N}}_l$, Total Population Size"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{R}}^{(l)}$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep
in defining formulation dp "$s(x, 0)$, Fraction Of Population Density Of Susceptibles"^^La Te X ep

Integral Of The Total Population Density (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfTheTotalPopulationDensityInitialCondition

integral of the total population density initial condition
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Total Population Density ni
contains quantity op Total Population Size ni
defining formulation dp "$\int_{\Omega^{(l)}} n(x) d x=\hat{\mathcal{N}}_l$"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{N}}_l$, Total Population Size"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Interaction Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionForce

interaction force on individual by media and influencers
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Interaction Force On An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionForceOnAnIndividual

interaction force on an individual
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Interaction Force ni
contains quantity op Interaction Weight ni
contains quantity op Medium Follower Matrix ni
contains quantity op Parameter To Scale Attractive Force From Influencers ni
contains quantity op Parameter To Scale Attractive Force From Media ni
contains quantity op Parameter To Scale Attractive Force From Other Individuals ni
contains quantity op Time ni
defining formulation dp "$F_i(\mathbf{x}, \mathbf{y}, \mathbf{z}, t)=\frac{a}{\sum_{j^{\prime}} w_{i j^{\prime}}(t)} \sum_{j=1}^N w_{i j}(t)\left(x_j(t)-x_i(t)\right)+b \sum_{m=1}^M B_{i m}(t)\left(y_m(t)-x_i(t)\right)+c \sum_{l=1}^L C_{i l}(t)\left(z_l(t)-x_i(t)\right)$"
in defining formulation dp "$B(t)$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$C(t)$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$F_i(t)$, Interaction Force"^^La Te X ep
in defining formulation dp "$a$, Parameter To Scale Attractive Force From Other Individuals"^^La Te X ep
in defining formulation dp "$b$, Parameter To Scale Attractive Force From Media"^^La Te X ep
in defining formulation dp "$c$, Parameter To Scale Attractive Force From Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$w_{ij}$, Interaction Weight"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "The interaction force on individual i is given by a weighted sum of attractive forces from all other connected individuals j, the respective media and the respective influencer scaled by the parameters a,b,c > 0 respectively."@en

Interaction Weightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionWeight

interaction weight between a pair of individuals to account for their influence on each other's opinions
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Interaction Weight Between Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionWeightBetweenIndividuals

interaction weights between pairs of individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Individual Relationship Matrix ni
contains quantity op Interaction Weight ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Pair Function ni
contains quantity op Time ni
defines op Interaction Weight ni
defining formulation dp "$ w_{ij}(t) = A_{ij}(t) \phi (|| x_j(t) - x_i(t)|| )$"^^La Te X ep
in defining formulation dp "$A(t)$, Individual Relationship Matrix"^^La Te X ep
in defining formulation dp "$\phi$, Pair Function"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$w_{ij}(t)$, Interaction Weight"^^La Te X ep
in defining formulation dp "$x(t)$, Opinion Vector of Individuals"^^La Te X ep
is space-continuous dp "true"^^boolean

Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateSubstrate2ComplexConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E*S_2}}{dt} = k_{3} c_{E*} c_{S_2} + k_{-4} c_{E} c_{P_2} - k_{-3} c_{E*S_2} - k_{4} c_{E*S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Intermediate - Substrate 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateSubstrate2ComplexConcentration

amount of intermediate - substrate 2 complex present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Intermediate Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateConcentration

amount of intermediate present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Intermediate Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E*}}{dt} = k_{2} c_{ES_1} + k_{-3} c_{E*S_2} - k_{-2} c_{E*} c_{P_1} - k_{3} c_{E*} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Intermolecular Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermolecularPotential

energy function that describes the interactions between molecules
belongs to
Quantity c
has facts
description ap "Intermolecular potential energy function that describes the interactions between molecules. Typically, Intermolecular forces are weak relative to intramolecular forces."@en
wikidata I D ap Q245031 ep

Ion Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IonCurrent

flow of electrical charge observed in electrolytes, wires, plasma, and other conducting materials or fluids
belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni
qudt I D ap Ion Current ep
wikidata I D ap Q6063423 ep

Irreversibility Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IrreversibilityAssumption

complexed enzyme concentration much higher than the product concentration
belongs to
Mathematical Formulation c
has facts
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Product Concentration ni
defining formulation dp "$\frac{c_{EX}}{c_P} \gg 1$"^^La Te X ep
in defining formulation dp "$c_P$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep

Isotropic Gaussian Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IsotropicGaussianFunction

Gaussian function representing density and density fractions of provinces
belongs to
Quantity c
has facts
description ap "Isotropic Gaussian Function located at the center of the respective province used in the PDE SEIR Model for representing density and density fractions"@en

Isotropic Gaussian Function Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IsotropicGaussianFunctionFormulation

isotropic gaussian function located at the center of the respective province for representing density and density fractions
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Center Of Province ni
contains quantity op Isotropic Gaussian Function ni
contains quantity op Pi Number ni
contains quantity op Variance ni
defining formulation dp "$G^{(l)}(x) \equiv \frac{1}{2\pi\sigma^2}\text{exp}(-\frac{||x-x_0^{(l)}||^2}{2\sigma^2})$"^^La Te X ep
in defining formulation dp "$G^{(l)}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$\pi$, Pi Number"^^La Te X ep
in defining formulation dp "$\sigma$, Variance"^^La Te X ep
in defining formulation dp "$x_0^{(l)}$, Center Of Province"^^La Te X ep

Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Jahnke_2022_Efficient_Numerical_Simulation_of_Soil-Tool_Interaction

publication
belongs to
Publication c
has facts
doi I D ap publica 340 ep

Koprucki (2017) Numerical methods for drift-diffusion modelsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Koprucki_2017_Numerical_methods_for_drift-diffusion_models

publication
belongs to
Publication c
has facts
description ap "Handbook of Optoelectronic Device Modeling and Simulation, Chapter = 50, Editor = Joachim Piprek, Pages = 733-771, Title = Drift-Diffusion Models, publisher = CRC Press, Volume = 2, Year = 2017"@en
doi I D ap W I A S. P R E P R I N T.2263 ep

Kostré (2022) Understanding the romanization spreading on historical interregional networks in Northern Tunisiani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Kostre_2022_Understanding_the_romanization_spreading_on_historical_interregional_networks_in_Northern_Tunisia

publication
belongs to
Publication c
has facts
invents op Susceptible Infectious Epidemic Spreading Model ni
studies op Romanization Spreading in Northern Tunesia ni
doi I D ap s41109 022 00492 w ep
wikidata I D ap Q115136310 ep

Lagrange Multiplierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LagrangeMultiplier

method to solve constrained optimization problems
belongs to
Quantity c
has facts
generalizes quantity op Control System Lagrange Multiplier ni
wikidata I D ap Q598870 ep

Laplace Equation For The Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LaplaceEquationForTheElectricPotential

in electrostatics, the Laplace equation characterizes the electrostatic potential in the absence of charges
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Permittivity (Dielectric) ni
generalized by formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$-\nabla\left(\epsilon_s\nabla\phi\right)=0$"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\phi$, Electric Potential"^^La Te X ep
wikidata I D ap Q339444 ep

Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Length

measured dimension of an object
belongs to
Quantity Kind c
has facts
qudt I D ap Length ep
wikidata I D ap Q36253 ep

Length Of Unit Cellni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LengthOfUnitCell

defines the size of the repeating unit in a crystal structure
belongs to
Quantity c
has facts
generalized by quantity op Length ni

Leskovac (2003) Comprehensive Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Leskovac_2003_Comprehensive_Enzyme_Kinetics

publication
belongs to
Publication c
has facts
surveys op Enzyme Kinetics ni
description ap "Vrvic, Miroslav. (2003). Comprehensive enzyme kinetics by V. Leskovac, Published by Kluwer Academic/Plenum Plblisher New York, March 2003-11-17. Journal of The Serbian Chemical Society - J SERB CHEM SOC. 68. 1011-1013"@en
doi I D ap J S C0312011 V ep

Level Of Mortalityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LevelOfMortality

rate at which individuals in a population die over a specified period
belongs to
Quantity c

Likelihood Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LikelihoodValue

probability density of observed data viewed as a function of the parameters of a statistical model
belongs to
Quantity c
has facts
description ap "measure used in statistics to quantify how well a given set of model parameters explains observed data"@en
wikidata I D ap Q45284 ep

Limiting Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingDistributionOfIndividuals

limiting distribution of individuals
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Limiting Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingDistributionOfIndividualsFormulation

equation representing the limiting distribution of individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains assumption op Number Of Individuals Tends To Infinity Assumption ni
contains quantity op Attraction Force At Opinion ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Rate Of Switching Influencers ni
contains quantity op Time ni
generalized by op Empirical Distribution Of Individuals Formulation ni
defining formulation dp "$\partial_t \rho_{m, l}(x, t)=\frac{1}{2} \sigma^2 \Delta \rho_{m, l}(x, t)-\nabla \cdot\left(\rho_{m, l}(x, t) \mathcal{F} \left(x, y_m, z_l, \rho\right)\right) \quad+\sum_{l^{\prime} \neq l}\left(-\Lambda_m^{\rightarrow l^{\prime}}(x, t) \rho_{m, l}(x, t)+\Lambda_m^{\rightarrow l}(x, t) \rho_{m, l^{\prime}}(x, t)\right)$"^^La Te X ep
in defining formulation dp "$\Lambda_m^{\rightarrow l}$, Rate Of Switching Influencers"^^La Te X ep
in defining formulation dp "$\mathcal{F}$, Attraction Force at Opinion"^^La Te X ep
in defining formulation dp "$\partial_t \rho_{m, l}(x, t)$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$\sigma$, Noise Strength"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
in defining formulation dp "$y_m$, Opinion"^^La Te X ep
in defining formulation dp "$z_l$, Opinion"^^La Te X ep

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrdered

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism in the backward direction."@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrderedDefinition

definition of a limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,b} \equiv \frac{k_{-1} k_{-2} k_{-3}}{k_{-1} k_{-2} + k_{-1} k_3 + k_{-1} k_{-3} + k_{-2} k_{-3}} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrdered

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism in the forward direction."@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedDefinition

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv \frac{k_3 k_4 k_5}{k_4 +k_5 + k_3 k_4 + k_3 k_5 + k_{-3} k_5} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedsingleCC

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism and single central Complex in the forward direction."@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedsingleCCDefinition

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv \frac{k_4 k_5}{k_4 +k_5} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate (Uni Uni Reaction - Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionBackward

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "Maximal initial reaction rate of Uni Uni Reaction in the backward direction."@en

Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionBackwardDefinition

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Backward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,b} \equiv k_{-2} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Uni Uni Reaction - Backward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Uni Uni Reaction - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForward

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "Maximal initial reaction rate of Uni Uni Reaction in the forward direction."@en

Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardDefinition

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv k_2 c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_2$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrderedsingleCC

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_2 = \frac{k_{-1} k_{-2}}{k_{-1} +k_{-2}} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionPingPong

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_{2} = \frac{k_{-1} k_{-3}}{k_{-1} + k_{-3}} c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionTheorellChance

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_2 = k_{-1} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionPingPong

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_{1} = \frac{k_{2} k_{4}}{k_{2} + k_{4}} c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_2$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionTheorellChance

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_1 = k_3 c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardWithInhibitor

limiting reaction rate
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "Forward Limiting Reaction Rate with Inhibitor in an Uni Uni Reaction"@en

Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardWithInhibitorDefinition

limiting reaction rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,I,f} \equiv k_{6} c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_0}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_{6}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Line Conceptni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineConcept

line concepts assign frequencies to lines of a line pool
belongs to
Mathematical Formulation c
has facts
contains quantity op Frequency ni
contains quantity op PTN Line ni
documented in op Gattermann (2017) Line pool generation ni
defining formulation dp "$(\mathcal{L},f)$"^^La Te X ep
in defining formulation dp "$\mathcal{L}$, PTNLine"^^La Te X ep
in defining formulation dp "$f_l$, Frequency"^^La Te X ep
description ap "A line concept is a set of lines together with their frequencies. The frequency of a line says how often service is offered along that line within a given time period (e.g., an hour, a day)."@en

Line Concept Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineConceptCosts

costs of a line concept
belongs to
Mathematical Formulation c
has facts
contains formulation op Line Concept ni
contains formulation op Line Costs Computation ni
contains quantity op Costs ni
contains quantity op Costs of Line Concept ni
contains quantity op Frequency ni
defining formulation dp "$cost(\mathcal{L},f)=\sum_{l \in \mathcal{L}} f_l \cdot cost_l$"^^La Te X ep
in defining formulation dp "$(\mathcal{L},f)$, Line Concept"^^La Te X ep
in defining formulation dp "$cost(\mathcal{L},f)$,Costs of Line Concept"^^La Te X ep
in defining formulation dp "$cost_l$, Costs"^^La Te X ep
in defining formulation dp "$f_l$, Frequency"^^La Te X ep
description ap "The costs for a line concept summarizing the costs of single lines multiplied by their frequencies."@en

Line Costs Computationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineCostsComputation

sum of all costs of a single line
belongs to
Mathematical Formulation c
has facts
contains quantity op Costs ni
contains quantity op Costs per Unit ni
contains quantity op Duration ni
contains quantity op Fixed Costs ni
contains quantity op Graph Type Identifier ni
contains quantity op Length ni
contains quantity op Period Length ni
contains quantity op Turn Over Time ni
defining formulation dp "$cost_l=costs\_fixed+\sum_{e \in l}\left(costs\_length \cdot length_e + costs\_edges\right) + costs\_vehicles \cdot \lvert x \cdot \frac{duration_l + turn\_over\_time}{period\_length}\rvert$"^^La Te X ep
in defining formulation dp "$cost_l$, Costs"^^La Te X ep
in defining formulation dp "$costs\_edges$, Costs"^^La Te X ep
in defining formulation dp "$costs\_fixed$, Fixed Costs"^^La Te X ep
in defining formulation dp "$costs\_length$, Costs per Unit"^^La Te X ep
in defining formulation dp "$costs\_vehicles$, Costs"^^La Te X ep
in defining formulation dp "$duration_l$, Duration"^^La Te X ep
in defining formulation dp "$length_e$, Length"^^La Te X ep
in defining formulation dp "$period\_length$, Period Length"^^La Te X ep
in defining formulation dp "$turn\_over\_time$, Turn Over Time"^^La Te X ep
in defining formulation dp "$x$,Graph Type Identifier"^^La Te X ep
description ap "The costs of a single line in public transport are made up of various individual costs."@en

Line Planningni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinePlanning

choosing subset of line from line pool to generate a line plan afterwards
belongs to
Research Problem c
has facts
contained in field op Transportation Planning ni
studied in op Gattermann (2017) Line pool generation ni

Linear Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Linear_Discrete_Element_Method

variant of the discrete element method that employs linear contact models for inter-particle forces
belongs to
Mathematical Model c
has facts
contained in model op Recurrent Neural Network Surrogate for Discrete Element Method ni
generalized by model op Discrete Element Method ni

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionDixonModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionEadieHofsteeModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionHanesWoolfModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionLineweaverBurkModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionDixonModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionEadieHofsteeModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionHanesWoolfModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionLineweaverBurkModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKineticsLinear

linear determination of the kinetic constants for enzyme-catalyzed reactions
belongs to
Computational Task c
has facts
doi I D ap B978 0 12 801238 3.05143 6 ep

Linear Rotorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotor

mathematical model of a linear molecule as a rigid rotor
belongs to
Mathematical Model c
has facts
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
approximates model op Linear Rotor (Non-Rigid) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalizes model op Linear Rotor (Apolar) ni
generalizes model op Linear Rotor (Polar) ni

Linear Rotor (Apolar)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorApolar

mathematical model of an apolar linear molecule as a rigid rotor, interacting through its induced dipole moment with electric fields
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalized by model op Linear Rotor (Combined) ni

Linear Rotor (Combined)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorCombined

mathematical model of a polar linear molecule as a rigid rotor, interacting through both its permanent and induced electric dipole moment with electric fields
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Conditional Quasi-Solvability ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
description ap "Note that under certain circumstances analytical solutions to the TISE are available for a finite number of low energy states (conditional quasi-exact solutions)"@en

Linear Rotor (Non-Rigid)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorNonRigid

modeling a linear molecule as a non-rigid rotor, i.e., the bond between the atoms stretches out as the molecule rotates faster
belongs to
Mathematical Model c
has facts
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Quantum Hamiltonian (Non-Rigid Rotor) ni

Linear Rotor (Polar)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorPolar

mathematical model of a polar linear molecule as a rigid rotor, interacting through its permanent dipole moment with electric fields
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalized by model op Linear Rotor (Combined) ni

Linear Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearStrain

relative change of length with respect the original length
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Strain ni
is dimensionless dp "true"^^boolean
qudt I D ap Linear Strain ep
wikidata I D ap Q1990546 ep

Linear Strain (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearStrainDefinition

relative change of length with respect the original length
belongs to
Mathematical Formulation c
has facts
contains quantity op Change In Length ni
contains quantity op Length ni
contains quantity op Linear Strain ni
defines op Linear Strain ni
defining formulation dp "$\varepsilon \equiv \frac{\Delta l}{l}$"^^La Te X ep
in defining formulation dp "$\Delta l$, Change In Length"^^La Te X ep
in defining formulation dp "$\varepsilon$, Linear Strain"^^La Te X ep
in defining formulation dp "$l$, Length"^^La Te X ep

Lineweaver (1934) The Determination of Enzyme Dissociation Constantsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Lineweaver_1934_The_Determination_of_Enzyme_Dissociation_Constants

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Steady State Assumption) ni
doi I D ap ja01318a036 ep

Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductSteadyStateAssumption

equation for uni uni reaction without product following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductIrreversibilityAssumption

equation for uni uni reaction without product following irreversibility assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

equation for uni uni reaction without product following rapid equilibrium assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without Product and competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S (1 + \frac{c_I}{K_{ic}})}{V_{max,f} c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}}+ \frac{K_m (1 + \frac{c_I}{K_{ic}})}{V_{max,f} c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}}+ \frac{K_m (1 + \frac{c_I}{K_{ic}})}{V_{max,f} c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}} + \frac{K_S}{V_{max,f} c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Link Recommendation Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinkRecommendationFunction

function representing link recommendation
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "Link recommendation algorithms are often used to suggest new connections to users that have the greatest potential to be established. In modelling Opinion Dynamics, link recommendation can be incorporated via this function by assuming that individuals have a higher chance of switching to an influencer with a structurally similar followership. Strictly increasing on [0,1]"@en

Liouville-von Neumann Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LiouvilleVonNeumannEquation

describes how a density operator (for pure or for mixed states) evolves in time
belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Time ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\frac{\partial\hat\rho}{\partial t} = -\frac{i}{\hbar}\left[\hat H, \hat\rho\right]$"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\hat{\rho}$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Just as the Schrödinger equation describes how pure states evolve in time, the Liouville-von Neumann equation describes how a density operator evolves in time. Note that there can be different density operators for pure or for mixed states."@en
description ap "Note the similarity with the classical Liouville equation where the commutator brackets [.,.] are replaced by Poisson brackets {.,.}"@en
alt Label ap "Quantum Liouville Equation"@en
alt Label ap "von Neumann equation"@en
wikidata I D ap Q2533076 ep

Logical Rule Extraction Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LogicalRuleExtractionFormulation

equation that extracts logical rules by determining the Gröbner basis of an ideal
belongs to
Mathematical Formulation c
has facts
contains quantity op Boolean Ring ni
contains quantity op Gröbner Basis ni
contains quantity op Ideal ni
defining formulation dp "$G = G(\langle\mathcal{B}\rangle)$"^^La Te X ep
in defining formulation dp "$G$, Gröbner Basis"^^La Te X ep
in defining formulation dp "$\langle\mathcal{B}\rangle$, Ideal"^^La Te X ep
in defining formulation dp "$\mathcal{B}$, Boolean Ring"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Lorentz Force Equation (Non-Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceEquationNonRelativistic

force exerted on a moving electric (point) charge in electromagnetic field (non-relativistic approach)
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Force ni
contains quantity op Classical Velocity ni
contains quantity op Electric Charge ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
defining formulation dp "$\boldsymbol{F} = q (\boldsymbol{E} + \boldsymbol{v} \times \boldsymbol{B})$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
wikidata I D ap Q172137 ep

Lorentz Force Equation (Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceEquationRelativistic

force exerted on a moving electric (point) charge in electromagnetic field (relativistic approach)
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Electric Charge ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Mass ni
contains quantity op Speed Of Light ni
contains quantity op Time ni
generalizes formulation op Lorentz Force Equation (Non-Relativistic) ni
defining formulation dp "$\frac{\mathrm{d} }{\mathrm{d}t} {m\mathbf{v} \over \sqrt{1-\left(\frac{\mathbf{v} }{c}\right)^2} } = q\left ( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right ) $"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
wikidata I D ap Q172137 ep

Lorentz Force Model (Non-Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceModelNonRelativistic

modeling the motion of "test charges" in electromagnetic fields in terms of the Lorentz force
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains formulation op Lorentz Force Equation (Non-Relativistic) ni
models op Particles In Electromagnetic Fields ni
description ap "Neglecting the fact that real particles would generate their own E and B fields, which would alter the electromagnetic forces that they experience."@en
description ap "Todo: Potential computational task: Calculate E and B fields from a given trajectory"@en
description ap "Todo: Potential computational task: Calculate trajectory from given E and B fields"@en
wikidata I D ap Q172137 ep

Lorentz Force Model (Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceModelRelativistic

modeling the motion of "test charges" in electromagnetic fields in terms of the Lorentz force
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains formulation op Lorentz Force Equation (Relativistic) ni
generalizes model op Lorentz Force Model (Non-Relativistic) ni
models op Particles In Electromagnetic Fields ni
description ap "Neglecting the fact that real particles would generate their own E and B fields, which would alter the electromagnetic forces that they experience."@en
description ap "Todo: Potential computational task: Calculate E and B fields from a given trajectory"@en
description ap "Todo: Potential computational task: Calculate trajectory from given E and B fields"@en
wikidata I D ap Q172137 ep

Loss Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunction

loss function summing over regions and data points
belongs to
Quantity c
has facts
defined by op Loss Function (Definition) ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q1036748 ep

Loss Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Loss_Function

in mathematical optimization, a function (to be minimized) representing the cost of each outcome
belongs to
Mathematical Model c
has facts
contained in model op Artificial Neural Network ni
wikidata I D ap Q1036748 ep

Loss Function (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunctionDefinition

loss function summing over regions and data points
belongs to
Mathematical Formulation c
has facts
contains quantity op Spreading Curve (Approximate) ni
contains quantity op Loss Function ni
contains quantity op Number of Regions ni
contains quantity op Number of Time Points ni
contains quantity op Romanized Cities Vector ni
contains quantity op Contact Network (Time-dependent) ni
contains quantity op Time Point ni
contains quantity op Weight Factor ni
defining formulation dp "$\ell (\sigma ) := \sum _{i=1}^{N_T} \sum _{m=1}^{N_R} \frac{(\omega _{m,t_i} - \phi (t_i| \sigma , \omega _{\bullet , 0}))^2 }{C_{m,t_i}^2}$"^^La Te X ep
in defining formulation dp "$C$, Weight Factor"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$N_T$, Number of Time Points"^^La Te X ep
in defining formulation dp "$\ell$, Loss Function"^^La Te X ep
in defining formulation dp "$\omega$, Romanized Cities Vector"^^La Te X ep
in defining formulation dp "$\phi$, Spreading Curve (Approximate)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t_i$, Time Point"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Loss Function Minimizationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunctionMinimization

minimization of loss function over regions and data points
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Loss Function ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\min _{\sigma =(G, \alpha )} \ell (\sigma )$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$\ell$, Loss Function"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Lumped Activation Parameterni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LumpedActivationParameter

lumped activation parameter
belongs to
Mathematical Formulation c
has facts
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
defining formulation dp "$\gamma = H \left( \mathbf{y}, \lambda_\text{f}, \dot{\lambda}_{\text{f}}\right)$"^^La Te X ep
in defining formulation dp "$\dot{\lambda}_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre stretch"^^La Te X ep
in defining formulation dp "$\mathbf{y}$, Vector of internal state variables"^^La Te X ep

Lyapunov Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquation

matrix equation used in the stability analysis of linear dynamical systems
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Lyapunov Equation Controllability ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$AX+XA^H+Q=0$"^^La Te X ep
in defining formulation dp "$A^H$, the conjugate transpose of A"^^La Te X ep
in defining formulation dp "$Q$, Hermitian matrix"^^La Te X ep
description ap "Numerical solution of a Lyapunov equation $AX+XA^T+B=0$ via Zhou and Sorensen 2-solve method, implemented as part of the Matrix Equation Sparse Solver (M.E.S.S.) project. Copyright 2009-2022 Jens Saak, Martin Koehler, Peter Benner and others."@en
doi I D ap S1110757 X03212055 ep
wikidata I D ap Q1028945 ep

Lyapunov Equation Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquationControllability

Lyapunov equation used in the stability analysis of linear dynamical systems to determine the controllability
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Gramian Matrix Controllability ni
similar to formulation op Lyapunov Equation Observability ni
defining formulation dp "$AW_c + W_cA^{*} + BB^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep
description ap "For the solvability of ordinary Lyapunov equations, the stability condition for A is the only requirement."@en

Lyapunov Equation Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquationObservability

Lyapunov equation used in the stability analysis of linear dynamical systems to determine the observability
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Gramian Matrix Observability ni
defining formulation dp "$A^{*}W_o + W_oA + C^*C = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep
description ap "For the solvability of ordinary Lyapunov equations, the stability condition for A is the only requirement."@en

Lyapunov Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovGeneralizedControllability

generalized Lyapunov equation used in the stability analysis of linear dynamical systems to determine the controllability
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Controllability ni
generalized by formulation op Lyapunov Equation ni
generalizes formulation op Lyapunov Equation Controllability ni
similar to formulation op Lyapunov Generalized Observability ni
defining formulation dp "$AW_c + W_cA^{*} + \sum_kN_kW_{c}N_k^{*} + BB^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Controllability"^^La Te X ep
description ap "For a numerical solution, one can resort to iterative schemes, which requires the solution of a standard Lyapunov equation in each step. As an alternative, one may use the biconjugate gradient method (with preconditioner) as suggested by Tobias Breiten from TU Graz, Austria, now TU Berlin."@en
description ap "For the solvability of generalized Lyapunov equations, there are two requirements: (1) stability condition for A and (2) suitable upper bound for the norm of N."@en

Lyapunov Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovGeneralizedObservability

generalized Lyapunov equation used in the stability analysis of linear dynamical systems to determine the observability
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Observability ni
generalized by formulation op Lyapunov Equation ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$A^{*}W_o + W_oA + \sum_k N_k^{*}W_{o}N_k + C^*C = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Observability"^^La Te X ep
description ap "For a numerical solution, one can resort to iterative schemes, which requires the solution of a standard Lyapunov equation in each step. As an alternative, one may use the biconjugate gradient method (with preconditioner) as suggested by Tobias Breiten from TU Graz, Austria, now TU Berlin."@en
description ap "For the solvability of generalized Lyapunov equations, there are two requirements: (1) stability condition for A and (2) suitable upper bound for the norm of N."@en

Magnetic Fieldni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MagneticField

spatial distribution of vectors allowing the calculation of the magnetic force on a test particle
belongs to
Quantity Kind c
has facts
qudt I D ap Magnetic Field Strength H ep
wikidata I D ap Q11408 ep

Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Mass

property of matter to resist changes of the state of motion and to attract other bodies
belongs to
Quantity Kind c
has facts
contained in formulation op Classical Newton Equation ni
qudt I D ap Mass ep
wikidata I D ap Q11423 ep

Mass Action Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MassActionLaw

rate of chemical reaction is directly proportional to the product of the activities or concentrations of the reactants
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Molecularity ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v = k \prod_{i=1}^{n} c_{i}$"^^La Te X ep
in defining formulation dp "$c_i$, Concentration"^^La Te X ep
in defining formulation dp "$k$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$n$, Molecularity"^^La Te X ep
in defining formulation dp "$v$, Reaction Rate"^^La Te X ep
wikidata I D ap Q899494 ep

Mass Balance Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MassBalanceLaw

mass that enters a system must, by conservation of mass, either leave the system or accumulate within the system
belongs to
Mathematical Formulation c
has facts
generalized by formulation op Conservation Law ni
defining formulation dp "$\delta_t + \nabla F = 0$"^^La Te X ep
wikidata I D ap Q3276889 ep

Material Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialDensity

measure of how much mass is contained within a given volume of a material
belongs to
Quantity c
has facts
generalized by quantity op Density ni

Material Point Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointAcceleration

acceleration experienced by material points in the Material Point Method
belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni

Material Point Displacementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointDisplacement

movement of material points
belongs to
Quantity c
has facts
generalized by quantity op Displacement ni
description ap "Material Point Displacement in the context of the Material Point Method (MPM) refers to the movement of material points, which are used to track physical information like mass and velocity."@en

Material Point Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointVelocity

velocity assigned to each material point within a simulation
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "Material Point Velocity in the context of the Material Point Method (MPM) refers to the velocity assigned to each material point within a simulation."@en

Mathematical Analysis of DHW Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalAnalysisOfDHWEquation

mathematical analysis of Darwin Howie Whelan equation for the scattering of fast electrons described by the Schrödinger equation.
belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
doi I D ap 21 M139164 X ep

Maximal Object Descriptiveness Ratingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaimalObjectDescriptivenessRating

maximal rating assigned to an object commonality in terms of object descriptiveness
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Maximizing Poisson log-Likelihoodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximizingPoissonLogLikelihood

maximizing Poisson log-likelihood of mortality models
belongs to
Computational Task c
has facts
applies model op Gamma-Gompertz-Makeham Model ni
contains formulation op Poisson log-Likelihood ni
contains input op Death Count ni
contains input op Exposure Of An Individual ni
contains output op Extrinsic Mortality ni
contains output op Heterogeneity of Death Rate ni
contains output op Level Of Mortality ni
contains output op Likelihood Value ni
contains output op Rate Of Aging ni
generalized by task op Maximum Likelihood Estimation ni

Maximum Isometric Muscle Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximumIsometricMuscleForce

greatest force a muscle can generate without changing its length
belongs to
Quantity c
has facts
generalized by quantity op Force ni

Maximum Likelihood Estimationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximumLikelihoodEstimation

estimating the parameters of a statistical model to fit given observations
belongs to
Computational Task c
has facts
wikidata I D ap Q1045555 ep

Maxwell Equations Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaxwellEquationsModel

set of four coupled partial differential equations describing how electric and magnetic fields are generated and altered by each other and by charges and currents
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains assumption op Nonrelativistic Approximation ni
description ap "Shalva: Given the charge density ρ(r, t) and the current density j(r, t), Maxwell's equations yield the electric and magnetic fields, E(r, t) and B(r, t). These equations are the simplest representative of a more general class of models, also referred as Maxwell's equations, where ρ(r, t) and j(r, t) should be found from certain additional relations, e.g., from the Ohm's law."@en
description ap "Together with the Lorentz force law, Maxwell's equations form the foundation of classical electromagnetism and optics. The equations provide a mathematical model for electric, optical, and radio technologies."@en
doi I D ap rstl.1865.0008 ep
wikidata I D ap Q51501 ep

Mechanical Deformationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalDeformation

in engineering or in continuum mechanics, any changes in the shape or size of a matter object
belongs to
Quantity Kind c
has facts
wikidata I D ap Q2672013 ep

Mechanical Deformation (Boundary Value)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalDeformationBoundaryValue

mechanical deformation at a domain boundary
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Deformation ni

Mechanical Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalStrain

in continuum mechanics, strain is defined as the relative deformation of matter caused by mechanical stress
belongs to
Quantity Kind c
has facts
generalizes quantity op Linear Strain ni
nondimensionalizes quantity op Mechanical Deformation ni
qudt I D ap Strain ep
wikidata I D ap Q3083131 ep

Mechanical Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalStress

internal forces caused by deformation of a continuous material
belongs to
Quantity Kind c
has facts
generalizes quantity op Eigenstress Of Crystal ni
generalizes quantity op Fluid Viscous Stress ni
generalizes quantity op Normal Stress ni
generalizes quantity op Stress Of Crystal ni
description ap "Has components shear stress, normal stress. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the constituent atoms or molecules."@en
qudt I D ap Stress ep
wikidata I D ap Q206175 ep

Medical Imagingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MedicalImaging

technique and process of creating visual representations of the interior of a body
belongs to
Research Field c
has facts
wikidata I D ap Q931309 ep

Medium Follower Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumFollowerMatrix

adjacency matrix for medium-follower relations
belongs to
Quantity c
has facts
generalized by quantity op Adjacency Matrix ni
is dimensionless dp "true"^^boolean

Medium Influencer Fractionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumInfluencerFraction

fraction of individuals following a specific medium and influencer at a given time
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "Fraction of individuals that follow a specific medium and influencer at a given time."@en

Medium Influencer Fraction Limitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumInfluencerFractionLimit

fraction of individuals following a specific medium and influencer at a given time with total number of Individuals tending to infinity
belongs to
Quantity c
has facts
generalized by op Medium Influencer Fraction ni

Membrane Capacitanceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MembraneCapacitance

how much charge a cell membrane can store when a voltage is applied across it
belongs to
Quantity c
has facts
generalized by quantity op Electric Capacitance ni

Michaelis (1913) Die Kinetik der Invertinwirkungni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Michaelis_1913_Die_Kinetik_der_Invertinwirkung

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni

Michaelis Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstant

property to characterize the kinetics of Michaelis–Menten reactions
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "Property to characterize the kinetics of Michaelis–Menten reactions"@en
wikidata I D ap Q61751178 ep

Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProductUniUniReactionSteadyStateAssumption

Michaelis constant for the product of an Uni Uni Reaction under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProductUniUniReactionSteadyStateAssumptionDefinition

Michaelis constant for the product of an Uni Uni Reaction under the Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P} \equiv \frac{k_{-1} + k_{2}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{P}$, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of the constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionOrderedsingleCCSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-1} k_{-2}}{k_{-5} (k_{-1} + k_{-2})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct1BiBiReactionOrderedSteadyStateAssumption

Michaelis constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct1BiBiReactionOrderedSteadyStateAssumptionDefinition

Michaelis constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} \equiv \frac{k_{-1} k_{-2} k_{-3}}{k_{-5} (k_{-1} k_{-2} + k_{-1} k_3 + k_{-1} k_{-3} + k_{-2} k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionPingPongSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-3} (k_{-1} + k_{2})}{k_{-2} (k_{-1} + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionTheorellChanceSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-1}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionOrderedsingleCCSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1} (k_{-2} + k_4)}{k_{-4} (k_{-1} + k_{-2})}$"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct2BiBiReactionOrderedSteadyStateAssumption

Michaelis constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct2BiBiReactionOrderedSteadyStateAssumptionDefinition

Michaelis constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} \equiv \frac{k_{-1} (k_{-2} k_{4} + k_{-2} k_{-3} + k_3 k_4)}{k_{-5} (k_{-1} k_{-2} + k_{-1} k_3 + k_{-1} k_{-3} + k_{-2} k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionPingPongSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1} (k_{-3} + k_{4})}{k_{-4} (k_{-1} + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionTheorellChanceSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1}}{k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionIrreversibilityAssumption

Michaelis constant for the substrate of an Uni Uni Reaction under the Irreversibility Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionIrreversibilityAssumptionDefinition

Michaelis constant for the substrate of an Uni Uni Reaction under the Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_2}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionRapidEquilibriumAssumption

Michaelis constant for the substrate of an Uni Uni Reaction under the Rapid Equilibrium Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionRapidEquilibriumAssumptionDefinition

Michaelis constant for the substrate of an Uni Uni Reaction under the Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionSteadyStateAssumption

Michaelis constant for the substrate of an Uni Uni Reaction under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionSteadyStateAssumptionDefinition

Michaelis constant for the substrate of an Uni Uni Reaction under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_{-1} + k_{2}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate1BiBiReactionOrderedSteadyStateAssumption

Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate1BiBiReactionOrderedSteadyStateAssumptionDefinition

Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} \equiv \frac{k_3 k_4 k_5}{k_1 (k_4 k_5 + k_3 k_4 + k_3 k_5 + k_{-3} k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionOrderedsingleCCSS

Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionOrderedsingleCCSSDefinition

Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} \equiv \frac{k_4 k_5}{k_1 (k_4 + k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionPingPongSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} = \frac{k_{4} (k_{-1} + k_{2})}{k_{1} (k_{2} + k_{4})}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionTheorellChanceSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} = \frac{k_{3}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate2BiBiReactionOrderedSteadyStateAssumption

Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate2BiBiReactionOrderedSteadyStateAssumptionDefinition

Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} \equiv \frac{k_5 (k_{-2} k_4 + k_{-2} k_{-3} + k_3 k_4)}{k_2 (k_4 k_5 + k_3 k_4 + k_3 k_5 + k_{-3} k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionOrderedsingleCCSS

Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionOrderedsingleCCSSDefinition

Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} \equiv \frac{k_5 (k_{-2} + k_4)}{k_2 (k_4 + k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
description ap "Definition of constant representing the concentration at which the reaction rate is half of its maximum value."@en

Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionPingPongSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} = \frac{k_{2} (k_{-3} + k_{4})}{k_{3} (k_{2} + k_{4})}$"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionTheorellChanceSS

constant representing the concentration at which the reaction rate is half of its maximum value
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} = \frac{k_{3}}{k_{2}}$"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct1SS

equation for bi bi reaction with ordered mechanism and product 1 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2}}{K_{iP_1}} c_{P_1} + c_{S_1} c_{S_2} + \frac{K_{S_1}}{K_{iP_1}} c_{S_2} c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct1SingleCCSS

equation for bi bi reaction with ordered mechanism and product 1 and single central complex following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Inhibition Constant ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2}}{K_{iP_1}} c_{P_1} + c_{S_1} c_{S_2} + \frac{K_{S_1}}{K_{iP_1}} c_{S_2} c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct2SS

equation for bi bi reaction with ordered mechanism and product 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2} K_{P_1}}{K_{iP_1} K_{P_2}} c_{P_2} + c_{S_1} c_{S_2} + \frac{K_{S_2} K_{P_1}}{K_{iP_1} K_{P_2}} c_{S_1} c_{P_2} + \frac{1}{K_{iP_2}} c_{S_1} c_{S_2} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct2SingleCCSS

equation for bi bi reaction with ordered mechanism and product 2 and single central complex following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Inhibition Constant ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2} K_{P_1}}{K_{iP_1} K_{P_2}} c_{P_2} + c_{S_1} c_{S_2} + \frac{K_{S_2} K_{P_1}}{K_{iP_1} K_{P_2}} c_{S_1} c_{P_2} + \frac{1}{K_{iP_2}} c_{S_1} c_{S_2} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProducts1and2SS

equation for bi bi reaction with ordered mechanism and products 1 and 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains quantity op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} V_{max,b} (c_{S_1} c_{S_2} - \frac{c_{P_1} c_{P_2}}{K_{eq}})}{V_{max,b} K_{iS_1} K_{S_2} + V_{max,b} K_{S_2} c_{S_1} + V_{max,b} K_{S_1} c_{S_2} + \frac{V_{max,f} K_{P_1}}{K_{eq}} c_{P_2} + \frac{V_{max,f} K_{P_2}}{K_{eq}} c_{P_1} + V_{max,b} c_{S_1} c_{S_2} + \frac{V_{max,f} K_{P_1}}{K_{iS_1} K_{eq}} c_{S_1} c_{P_2} + \frac{V_{max,f}}{K_{eq}} c_{P_1} c_{P_2} + \frac{V_{max,b} K_{S_1}}{K_{iP_1}} c_{S_1} c_{P_1} + \frac{V_{max,b}}{K_{iP_2}} c_{S_1} c_{S_2} c_{P_2} + \frac{V_{max,f}}{K_{iS_2} K_{eq}} c_{S_2} c_{P_1} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProducts1and2SingleCCSS

equation for bi bi reaction with ordered mechanism and products 1 and 2 and single central complex following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_0 = \frac{V_1 V_2 (c_{S_1} c_{S_2} - \frac{c_{P_1} c_{P_2}}{K_{eq}})}{V_2 K_{iS_1} K_{S_2} + V_2 K_{S_2} c_{S_1} + V_2 K_{S_1} c_{S_2} + \frac{V_1 K_{P_1}}{K_{eq}} c_{P_2} + \frac{V_1 K_{P_2}}{K_{eq}} c_{P_1} + V_2 c_{S_1} c_{S_2} + \frac{V_1 K_{P_1}}{K_{iS_1} K_{eq}} c_{S_1} c_{P_2} + \frac{V_1}{K_{eq}} c_{P_1} c_{P_2} + \frac{V_2 K_{S_1}}{K_{iP_1}} c_{S_1} c_{P_1} + \frac{V_2}{K_{iP_2}} c_{S_1} c_{S_2} c_{P_2} + \frac{V_1}{K_{iS_2} K_{eq}} c_{S_2} c_{P_1} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_1$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$V_2$, Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex)"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ordered without Products - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithoutProductsSS

equation for bi bi reaction with ordered mechanism and without products following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} +K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered without Products and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithoutProductsSingleCCSS

equation for bi bi reaction with ordered mechanism without products and single central complex following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_0 = \frac{V_1 c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} +K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_1$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationBiBiReactionPingPongMechanismwithProduct1SS

equation for bi bi reaction with ping pong mechanism with product 1 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{1} c_{S_1} c_{S_2}}{K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2}}{K_{iP_1}} c_{P_1} + \frac{K_{S_2}}{K_{iP_1}} c_{S_1} c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithProduct2SS

equation for bi bi reaction with ping pong mechanism with products 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
similar to formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{1} c_{S_1} c_{S_2}}{K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2} + \frac{K_{S_1} K_{iS_2}}{K_{iP_2}} c_{P_2} + \frac{K_{S_1}}{K_{iP_2}} c_{S_1} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithProducts1and2SS

equation for bi bi reaction with ping pong mechanism with products 1 and 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_{1} V_{2} (c_{S_1} c_{S_2} - \frac{c_{P_1} c_{P_2}}{K_{eq}})}{V_{2} K_{S_2} c_{S_1} + V_{2} K_{S_1} c_{S_2} + \frac{V_{1} K_{P_2}}{K_{eq}} c_{P_2} + \frac{V_{1} K_{P_1}}{K_{eq}} c_{P_2} + V_{2} c_{S_1} c_{S_2} + \frac{V_{1} K_{P_2}}{K_{iS_1} K_{eq}} c_{S_1} c_{P_1} +\frac{V_{1}}{K_{eq}} c_{P_1} c_{P_2} + \frac{V_{2} K_{S_1}}{K_{iP_2}} c_{S_2} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$V_{2}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithoutProductsSS

equation for bi bi reaction with ping pong mechanism without products following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "${v_0}=\frac{V_{1}*c_{S_1}*c_{S_2}}{K_{S_2}*c_{S_1}+K_{S_1}*c_{S_2}+c_{S_1}*c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_{0}$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProduct1SS

equation for bi bi reaction with Theorell-Chance mechanism with product 1 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2} + \frac{K_{S_1} K_{iS_2}}{K_{iP_1}} c_{P_1} + \frac{K_{S_2}}{K_{iP_1}} c_{S_1} c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProduct2SS

equation for bi bi reaction with Theorell-Chance mechanism with product 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2} + \frac{K_{iS_1} K_{S_2}}{K_{iP_2}} c_{P_2} + \frac{K_{S_1}}{K_{iP_2}} c_{S_2} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProducts1and2SS

equation for bi bi reaction with Theorell-Chance mechanism with products 1 and 2 following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_{1} V_{2} (c_{S_1} c_{S_2} - \frac{c_{P_1} c_{P_2}}{K_{eq}})}{V_2 K_{iS_1} K_{S_2} + V_2 K_{S_2} c_{S_1} + V_2 K_{S_1} c_{S_2} + \frac{V_1 K_{P_2}}{K_{eq}} c_{P_1} + \frac{V_1 K_{P_1}}{K_{eq}} c_{P_2} + V_2 c_{S_1} c_{S_2} + \frac{V_1 K_{P_2}}{K_{iS_1} K_{eq}} c_{S_1} c_{P_1} + \frac{V_2 K_{S_1}}{K_{iP_2}} c_{S_2} c_{P_2} + \frac{V_1}{K_{eq}} c_{P_1} c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$V_{2}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance without Products - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithoutProductsSS

equation for bi bi reaction with Theorell-Chance mechanism without products following steady state assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 c_{S_1} c_{S_2}}{K_{iS_1} K_{S_2} + K_{S_2} c_{S_1} + K_{S_1} c_{S_2} + c_{S_1} c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Uni Uni Reaction with Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithProductSteadyStateAssumption

equation for uni uni reaction with product following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Backward) ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_{0}=\frac{\frac{V_{max,f}}{K_{S}}*c_{S}-\frac{V_{max,b}}{K_{P}}*c_{P}}{1+\frac{c_{S}}{K_{S}}+\frac{c_{P}}{K_{P}}}$"^^La Te X ep
in defining formulation dp "$K_{P}$, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Uni Uni Reaction - Backward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_P$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_{0}$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductSteadyStateAssumption

equation for uni uni reaction without product following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductIrreversibilityAssumption

equation for uni uni reaction without product following irreversibility assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

equation for uni uni reaction without product following rapid equilibrium assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_S}{c_S + K_S (1 + \frac{c_I}{K_{ic}})}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandCompetitivePartialInhibitionSteadyStateAssumption

equation for uni uni reaction without product and competitive partial inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_S}{K_S \frac{(1+\frac{c_I}{K_{ic}})}{(1+\frac{c_I}{K_{iu}})} + C_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_S}{K_S (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandMixedPartialInhibitionSteadyStateAssumption

equation for uni uni reaction without product and mixed partial inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f} c_I}{K_{iu}}) c_S}{K_S (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
similar to formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_S}{(1 + \frac{c_I}{K_{ic}}) K_S + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandNonCompetitivePartialInhibitionSteadyStateAssumption

equation for uni uni reaction without product and non-competitive partial inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
similar to formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f} c_I}{K_{iu}}) c_S}{K_S (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive complete inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} c_S}{K_S + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandUncompetitivePartialInhibitionSteadyStateAssumption

equation for uni uni reaction without product and uncompetitive partial inhibition following steady state assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f}*c_I}{K_{iu}}) c_S}{K_S + (1 + \frac{c_I}{K_{iu}}) c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MixedEnzymeInhibitionCouplingConditionUniUniReaction

coupling condition for a mixed enzyme inhibition in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
defining formulation dp "$K_{ic} \neq K_{iu}$"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Mobility Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MobilityOfElectrons

magnitude of the drift velocity of electrons per unit electric field
belongs to
Quantity c
has facts
description ap "For use in semiconductor physics"@en

Mobility Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MobilityOfHoles

measure of how easily holes can move through the material under the influence of an electric field
belongs to
Quantity c
has facts
description ap "For use in semiconductor physics"@en

Model Order Reductionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ModelOrderReduction

technique in mathematical modeling to effectively reduce the dimensionality of a model
belongs to
Computational Task c
has facts
generalizes task op Balanced Truncation ni
generalizes task op H2 Optimal Approximation ni
description ap "After spatial discretization of PDEa, solving the resulting large-scale systems of ODEs can therefore become incredibly time-consuming. Developed from well established mathematical theory and robust numerical algorithms, Model Order Reduction (MOR) has been recognized as very efficient for reducing the simulation time of large-scale systems"@en
doi I D ap 978 1 4471 5102 9 142 1 ep
wikidata I D ap Q12202921 ep

Molecular Alignmentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularAlignment

expectation value indicating in how far molecular axes are parallel to space fxed axes
belongs to
Mathematical Formulation c
has facts
contains quantity op Polar Angle ni
contains quantity op Quantum State Vector ni
defining formulation dp "$A = \langle \psi | \cos^2 \theta | \psi \rangle$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
description ap "Typically achieved by the interaction of induced dipole moments with external laser fields"@en

Molecular Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Molecular_Dynamics

physical movements of atoms and molecules in a gas, a liquid, a solid, etc
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
generalizes problem op Molecular Reaction Dynamics ni
modeled by op Classical Dynamics Model ni
modeled by op Classical Langevin Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
modeled by op Quantum Model (Open System) ni
wikidata I D ap MathModDB Ontology ep

Molecular Orientationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularOrientation

expectation value indicating in how far molecular axes point in the same direction as space fxed axes
belongs to
Mathematical Formulation c
has facts
contains quantity op Polar Angle ni
contains quantity op Quantum State Vector ni
defining formulation dp "$O = \langle \psi | \cos \theta | \psi \rangle$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
description ap "Typically achieved by the interaction of permanent dipole moments with external electrostatic fields."@en

Molecular Physicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularPhysics

study of the physical properties of molecules.Significant overlaps with physical chemistry, chemical physics, and quantum chemistry
belongs to
Research Field c
has facts
contains problem op Molecular Reaction Dynamics ni
contains problem op Molecular Rotation ni
contains problem op Molecular Spectroscopy ni
contains problem op Molecular Spectroscopy (Transient) ni
contains problem op Molecular Spectrosopy (Stationary) ni
contains problem op Molecular Vibration ni
contains problem op Molecular Dynamics ni
wikidata I D ap Q489328 ep

Molecular Reaction Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularReactionDynamics

branch of physical chemistry that deals with observing and understang chemical reactions in real time and on an atomistic basis
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
description ap "Although there were first attempts in the 1930s (first trajectory calculations for H+H2 reaction calculated by Polanyi in Berlin-Dahlem), this field has strongy evolved since the 1970s and 1980s with the upcoming of short laser pulses."@en

Molecular Rotationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularRotation

rotation of a molecule about its center of mass. Often, molecules are assumed to rotate like rigid bodies, but there can also be centrifugal distortion
belongs to
Research Problem c
has facts
generalized by problem op Molecular Spectroscopy ni
modeled by op Linear Rotor (Apolar) ni
modeled by op Linear Rotor (Combined) ni
modeled by op Linear Rotor (Non-Rigid) ni
modeled by op Linear Rotor (Polar) ni
wikidata I D ap Q1234926 ep
wikidata I D ap Q904380 ep

Molecular Spectroscopyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectroscopy

measurement (or simulation) of interactions between electromagnetic waves and matter
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
generalizes problem op Molecular Spectroscopy (Transient) ni
generalizes problem op Molecular Spectrosopy (Stationary) ni
description ap "Rotations are collective motions of the atomic nuclei and typically lead to spectra in the microwave and millimeter-wave spectral regions. Vibrations are relative motions of the atomic nuclei and are studied by both infrared and Raman spectroscopy. Electronic excitations are studied using visible and ultraviolet spectroscopy as well as fluorescence spectroscopy"@en
wikidata I D ap Q1943412 ep

Molecular Spectroscopy (Transient)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectroscopyTransient

observing molecular dynamics by spectroscopy in real time
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
description ap "This discipline evolved since the 1980s, with the upcoming of pico-second, femto-second and eventually even atto-second laser pulses."@en

Molecular Spectrosopy (Stationary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectrosopyStationary

studying molecular energy levels by stationary, i.e. time-independent molecular spectrosopy
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
modeled by op Quantum Model (Open System) ni
description ap "For example, molecular vibrational states can be detected by infrared or Raman spectroscopy"@en

Molecular Vibrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularVibration

periodic motion of the atoms of a molecule around their equilibrium positions
belongs to
Research Problem c
has facts
generalized by problem op Molecular Spectroscopy ni
modeled by op Normal Modes ni
modeled by op Normal Modes (Anharmonic) ni
modeled by op Normal Modes (Harmonic) ni
modeled by op Normal Modes (Intermolecular) ni
description ap "Often modeled within the harmonic approximation, but there can be also effects of anharmonicity"@en
wikidata I D ap Q900121 ep

Molecularityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Molecularity

number of reactant molecular entities that are involved in the 'microscopic chemical event' constituting an elementary reaction
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q776329 ep

Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Momentum

conserved physical quantity related to the motion of a body
belongs to
Quantity Kind c
has facts
qudt I D ap Momentum ep
wikidata I D ap Q41273 ep

Momentum Balance Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MomentumBalanceEquation

in the theory of elasticity, the conservation of momentum can also be written in vector form
belongs to
Mathematical Formulation c
has facts
contains quantity op Eigenstress Of Crystal ni
contains quantity op Stress Of Crystal ni
defining formulation dp "$\nabla\cdot(\sigma-\sigma^\ast)=0$"^^La Te X ep
in defining formulation dp "$\sigma$, Stress Of Crystal"^^La Te X ep
in defining formulation dp "$\sigma^\ast$, Eigenstress Of Crystal"^^La Te X ep
description ap "These equations are known as the momentum balance equations because the momentum fluxes are balanced by body and surface forces."@en

Monodomain Equation for Action Potential Propagationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Monodomain_Equation_for_Action_Propagation_Potential

describes the evelution of the transmembrane potential at each sacomeres location i.e. the propagation of the action potential
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Action Potential Propagation Model ni
contains quantity op Effective Conductivity ni
contains quantity op Ion Current ni
contains quantity op Membrane Capacitance ni
contains quantity op Time ni
contains quantity op Transmembrane Potential ni
defining formulation dp "$$\frac{\partial V^\text{f}_\text{m}}{\partial t} = \frac{1}{C^\text{f}_\text{m}} \left( \frac{1}{A_\text{m}} \sigma_{\text{eff}} \frac{\partial^2 V^{\text{f}}_{\text{m}}}{\partial s^2} - I_\text{ion} (V^{\text{f}}_{\text{m}}, \mathbf{y}) + S(V^{\text{s}}_{\text{m}})\right)~ \text{in $\Omega_{f}$}$$"^^La Te X ep
in defining formulation dp "$C^{\text{f}}_{\text{m}}$, Membrane Capacitance"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion Current"^^La Te X ep
in defining formulation dp "$V^{\text{f}}_{\text{m}}$, Transmembrane Potential"^^La Te X ep
in defining formulation dp "$\sigma_{\text{eff}}$, Effective Conductivity"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

MOR Transformation Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MOR_TransformationMatrix

transformation matrix, to be applied to the input-output formulation of linear or bilinear control systems
belongs to
Quantity c

Mortality Modelingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MortalityModeling

science of determining likely future mortality rates
belongs to
Research Problem c
has facts
modeled by op Gamma-Gompertz-Makeham Model ni

Motor Neuron Pool Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Motor_Neuron_Pool_Model

mathematical model of neuromuscular system based on the agonist-antagonist myoneural interface
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is time-continuous dp "true"^^boolean
doi I D ap gamm.202370009 ep

Motor Neuron Pool ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Motor_Neuron_Pool_ODE_System

two coupled ODEs which describe the transmembrane potentials
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Motor Neuron Pool Model ni
contains quantity op Coupling Current ni
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
contains quantity op Ion Current ni
contains quantity op Membrane Capacitance ni
contains quantity op Neural Input ni
contains quantity op Sensory Organ Current ni
contains quantity op Time ni
contains quantity op Transmembrane Potential ni
defining formulation dp "$\begin{align} \frac{\text{d}V^{\text{d}}_{\text{m}}}{\text{d}t} &= \frac{1}{C^{\text{d}}_{\text{m}}}\left(-I^{\text{d}}_{\text{ion}}(V^{\text{d}}_{\text{m}}) - I^{\text{d}}_{\text{C}}(V^{\text{d}}_{\text{m}},V^{\text{s}}_{\text{m}}) \right) \\ \frac{\text{d}V^{\text{s}}_{\text{m}}}{\text{d}t} &= \frac{1}{C^{\text{s}}_{\text{m}}}\left(-I^{\text{s}}_{\text{ion}}(V^{\text{s}}_{\text{m}}) - I^{\text{s}}_{\text{C}}(V^{\text{d}}_{\text{m}},V^{\text{s}}_{\text{m}}) + I_{\text{spindle}}(\lambda_{\text{f}}, \dot{\lambda}_\text{f}) + I_\text{ext} \right) \\ \end{align}$"^^La Te X ep
in defining formulation dp "$t$, Time"
in defining formulation dp "$C_{\text{m}}$, Membrane Capacitance"^^La Te X ep
in defining formulation dp "$I_{\text{C}}$, Coupling Current"^^La Te X ep
in defining formulation dp "$I_{\text{ext}}$, Neural Input"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion Current"^^La Te X ep
in defining formulation dp "$I_{\text{spindle}}$, Sensory Organ Current"^^La Te X ep
in defining formulation dp "$V_{\text{m}}$, Transmembrane Potential"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Stretch"^^La Te X ep
description ap "Transmembrane potentials in the soma and the dendrite compartments."@en

Multi-Population Discrete Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousModel

discrete-time multi-population susceptible infectious model
belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Multi-Population Discrete Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousRemovedModel

discrete-time multi-population susceptible infectious removed model
belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Removed Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Multi-Population Discrete Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousSusceptibleModel

discrete-time multi-population susceptible infectious susceptible model
belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Multipolar Expansion Model (3D)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultipolarExpansionModel3D

mathematical series approximating an angle-dependent function
belongs to
Mathematical Model c
has facts
applied by task op Far Field Radiation ni
contains formulation op Spherical Harmonics Expansion (3D) ni
generalized by model op Maxwell Equations Model ni
models op Electromagnetic Fields And Waves ni
description ap "Multipole expansions are often used to represent electromagnetic fields, where the fields at distant points are given in terms of sources (charges and/or currents) in a small region (far field limit). The first term is called the monopole moment, the second term is called the dipole moment, the third term the quadrupole moment, etc."@en
wikidata I D ap Q1027847 ep

Muscle Contraction Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleContractionVelocity

muscle contraction velocity
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni

Muscle Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleLength

length of a muscle
belongs to
Quantity c
has facts
generalized by quantity op Length ni

Muscle Movementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Muscle_Movement

process in which force is generated within muscle tissue, resulting in a change in muscle geometry
belongs to
Research Problem c
has facts
wikidata I D ap "https://www.wikidata.org/wiki/Q127006"@en

Muscle Spindle Firing Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleSpindleFiringRate

frequency at which sensory neurons within the muscle spindle transmit signals to the central nervous system
belongs to
Quantity c
has facts
generalized by quantity op Neural Firing Rate ni

Near Field Radiationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NearFieldRadiation

electromagnetic radiation behaviors that predominate at shorter distances
belongs to
Computational Task c
has facts
applies model op Maxwell Equations Model ni
description ap "The near field is a region of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scatterer."@en
wikidata I D ap Q6984336 ep

Neumann Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryCondition

boundary condition specifying the values of derivatives of a solution of a differential equation along the boundaries of a domain
belongs to
Mathematical Formulation c
has facts
alt Label ap "second-type boundary condition"@en
wikidata I D ap Q1149279 ep

Neumann Boundary Condition (Stress-Free Relaxation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionStressFreeRelaxation

Neumann boundary condition in theory of elasticity (stress-free relaxation)
belongs to
Mathematical Formulation c
has facts
contains quantity op Eigenstress Of Crystal ni
contains quantity op Stress Of Crystal ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$(\sigma-\sigma^\ast)\cdot n=0$"^^La Te X ep
in defining formulation dp "$\sigma$, Stress Of Crystal"^^La Te X ep
in defining formulation dp "$\sigma^\ast$, Eigenstress Of Crystal"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep

Neumann Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionElectricPotential

Typically used to indicate that the electric field should be perpendicalar to an electrode interface
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Electrode Interfaces ni
contains quantity op Time ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \psi(r,t)|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Neumann Boundary Condition For Electron Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForElectronFermiPotential

Neumann boundary condition for the Fermi potential governing the electrons
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Drift-Diffusion Model ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \psi|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep

Neumann Boundary Condition For Hole Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForHoleFermiPotential

Neumann boundary condition for the Fermi potential governing the holes
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Drift-Diffusion Model ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \phi_p|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep

Neumann Boundary Condition For SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForSEIRModel

Neumann boundary condition for SEIR model
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op PDE SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
generalized by op Neumann Boundary Condition ni
defining formulation dp "$s + e + i + r = 1$"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
description ap "Homogeneous Boundary Condition For the Full-PDe SEIR Model ensure that all the fractions of the population densities of susceptibles, exposed, infectious and removed add up to 1 at all times"

Neural Firing Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeuralFiringRate

average number of electrical impulses, or spikes, a neuron generates per unit of time
belongs to
Quantity c
has facts
generalized by quantity op Frequency ni
wikidata I D ap Q71762818 ep

Neural Inputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeuralInput

neural input in a motor neuron pool model
belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni

Nodesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Nodes

set of all nodes in a graph
belongs to
Quantity c
has facts
contained in formulation op Public Transportation Network ni
wikidata I D ap "https://www.wikidata.org/wiki/Q124247078"

Noise Strengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NoiseStrength

noise modelling unknown external influences
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "noise caused by influences, uncertainties in the communication between individuals or free will"@en

Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NoncompetitiveEnzymeInhibitionCouplingConditionUniUniReaction

coupling condition for a non-competitive enzyme inhibition in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
defining formulation dp "$\begin{align} k_{1} &= k_{5} \\ k_{-1} &= k_{-5} \\ k_{-3} &= k_{-4}\\ k_{3} &= k_{4} \\ K_{ic} &= K_{iu}\\ \end{align}$"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_1$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_3$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$,Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Non-Local Meansni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonLocalMeans

algorithm in image processing for image denoising
belongs to
Mathematical Formulation c
has facts
defining formulation dp "$u(p) = {1 \over C(p)}\int_\Omega v(q) f(p,q)dq$"^^La Te X ep
in defining formulation dp "$C(p)$, a normalizing factor"^^La Te X ep
in defining formulation dp "$\Omega$, the area of an image"^^La Te X ep
in defining formulation dp "$f(p,q)$, the weighting function"^^La Te X ep
in defining formulation dp "$u(p)$, filtered value of the iamge at point $p$"^^La Te X ep
in defining formulation dp "$v(q)$, the unfiltered value of the image at point $q$"^^La Te X ep
doi I D ap C V P R.2005.38 ep
wikidata I D ap Q7048948 ep

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMIrreversibility

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMRapidEquilibrium

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMSteadyState

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandCompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandMixedCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandMixedPartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandNonCompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandUncompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKineticsNonlinear

nonlinear determination of the kinetic constants for enzyme-catalyzed reactions
belongs to
Computational Task c
has facts
is linear dp "false"^^boolean
doi I D ap B978 0 12 801238 3.05143 6 ep

Nonrelativistic Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonrelativisticApproximation

Newtonian dynamics as an approximation to special relativity
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Classical Dynamics Model ni
contained as assumption in op Classical Hamilton Equations ni
contained as assumption in op Classical Newton Equation ni
contains quantity op Classical Momentum ni
contains quantity op Relativistic Momentum ni
defining formulation dp "$p_{rel} \approx p_{cl}$"^^La Te X ep
in defining formulation dp "$p_{cl}$, Classical Momentum"^^La Te X ep
in defining formulation dp "$p_{rel}$, Relativistic Momentum"^^La Te X ep

Normal Interaction Force Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Normal_Interaction_Force_Of_Two_Particles

force component acting normally at the contact interface between two particles
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
contains quantity op Young Modulus ni
defining formulation dp "$\boldsymbol F^N_{ij}=\left(k_{ij}^N\delta_{ij}+d_{ij}^N\dot{\delta}_{ij}\right)\boldsymbol n_{ij}$ $\delta_{ij}=\langle \boldsymbol x_i - \boldsymbol x_j, \boldsymbol n_{ij}\rangle$ $\delta_{ij}=\langle \boldsymbol v_i - \boldsymbol v_j, \boldsymbol n_{ij}\rangle$ $\boldsymbol n_{ij} = \frac{\boldsymbol x_i - \boldsymbol x_j}{\lVert \boldsymbol x_i - \boldsymbol x_j \rVert}$ $k^N_{ij}=E_N \pi r_{ij} / 2$ $d_{ij}^N=D_N 2 \sqrt{k^N_{ij}m_{ij}}$ $m_{ij}=\frac{m_im_j}{m_i + m_j}$"^^La Te X ep
in defining formulation dp "$D_N$, control parameter of critical damping"^^La Te X ep
in defining formulation dp "$E_N$, Young Modulus"^^La Te X ep
in defining formulation dp "$\boldsymbol F^N_{ij}$, total normal force between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\boldsymbol v_i\in \mathbb R^3$, velocity of particle $i$ $\boldsymbol v_j\in \mathbb R^3$, velocity of particle $j$"^^La Te X ep
in defining formulation dp "$\boldsymbol x_i\in \mathbb R^3$, position of center of gravity for particle $i$ $\boldsymbol x_j\in \mathbb R^3$, position of center of gravity for particle $j$"^^La Te X ep
in defining formulation dp "$r_{ij}=(r_i+r_j)/2$, mean radius of particles $i$ and $j$"^^La Te X ep

Normal Mode Coordinateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinate

pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation
belongs to
Quantity c
has facts
description ap "Normal coordinates refer to the positions of atoms away from their equilibrium positions, wrt a normal mode of vibration. Formally, normal modes are determined by solving a secular determinant, and then the normal coordinates can be expressed as a summation over the cartesian coordinates (over the atom positions). The normal modes diagonalize the matrix governing the molecular vibrations."@en
wikidata I D ap Q112730947 ep

Normal Mode Coordinate (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinateDimensionless

nondimensionalized positions of atoms away from their equilibrium positions, wrt a normal mode of vibration
belongs to
Quantity c
has facts
defined by op Normal Mode Coordinate (Dimensionless, Definition) ni
nondimensionalizes quantity op Normal Mode Coordinate ni

Normal Mode Coordinate (Dimensionless, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinateDefinition

nondimensionalized positions of atoms away from their equilibrium positions, wrt a normal mode of vibration
belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Coordinate ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Planck Constant ni
contains quantity op Speed Of Light ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$\begin{align} q&=&\sqrt{\gamma}Q \\ \gamma&=&\frac{2 \pi c \omega}{\hbar} \end{align}$"^^La Te X ep
in defining formulation dp "$Q$, Normal Mode Coordinate"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep

Normal Mode Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentum

canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules
belongs to
Quantity c
has facts
wikidata I D ap Q112730947 ep

Normal Mode Momentum (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentumDimensionless

dimensionless canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules
belongs to
Quantity c
has facts
defined by op Normal Mode Momentum (Dimensionless, Definition) ni
nondimensionalizes quantity op Normal Mode Momentum ni

Normal Mode Momentum (Dimensionless, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentumDefinition

dimensionless canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules
belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Momentum ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Planck Constant ni
contains quantity op Speed Of Light ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$\begin{align} p&=&\frac{1}{\sqrt{\gamma}\hbar}P \\ \gamma&=&\frac{2 \pi c \omega}{\hbar} \end{align}$"^^La Te X ep
in defining formulation dp "$P$, Normal Mode Momentum"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep

Normal Modesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModes

describing molecular (or other) vibrations of many-body systems in terms of normal modes
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Hamiltonian (Normal Mode) ni
generalizes model op Normal Modes (Anharmonic) ni
generalizes model op Normal Modes (Harmonic) ni
generalizes model op Normal Modes (Intermolecular) ni
description ap "These coordinates can be constructed by means of the GF (or FG) method by Wilson."@en
description ap "To be done: Add equations etc. for the GF method"
wikidata I D ap Q3333538 ep

Normal Modes (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesAnharmonic

molecular (or other) vibrations of many-body systems in terms of normal modes, beyond the harmonic approximation
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Anharmonic) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
generalizes model op Normal Modes (Harmonic) ni
description ap "Describing molecular (or other) vibrations of many-body systems in terms of normal modes, beyond the harmonic approximation"@en

Normal Modes (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesHarmonic

describing molecular vibrations of many-body systems in terms of normal modes, within the harmonic approximation
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Harmonic) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Harmonic) ni

Normal Modes (Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesIntermolecular

describing molecular vibrations in terms of normal modes, beyond the harmonic approximation, and including intermolecular interactions
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Intermolecular) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Intermolecular) ni
generalizes model op Normal Modes (Anharmonic) ni
description ap "thus describing cluster effects, solvent effects etc."@en
doi I D ap tf9605600753 ep
doi I D ap zenodo.12805933 ep

Normal Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalStress

force component perpendicular to a surface element divided by the area of that surface element
belongs to
Quantity c
has facts
qudt I D ap Normal Stress ep
wikidata I D ap Q11425837 ep

Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberDimensionless

mathematical object used to count, label, and measure
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q11563 ep

Number of Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfCities

number of cities in region
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Exposed Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfExposedIndividuals

number of exposed individuals
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Exposed Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfExposedIndividualsFormulation

equation for the number of exposed individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Exposed Individuals ni
defining formulation dp "$\hat{\mathcal{E}}^{(l)} = \Sigma_{\mathcal{E}} \hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{E}}^{(l)}$, Number Of Exposed Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep

Number Of Individuals Tends To Infinity Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfIndividualsTendsToInfinityAssumption

assumption for the individual number
belongs to
Mathematical Formulation c
has facts
contains quantity op Total Number Of Individuals ni
defining formulation dp "$N \rightarrow \inf$"^^La Te X ep
in defining formulation dp "$N$, Total Number Of Individuals"^^La Te X ep

Number Of Infected Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfInfectedCities

number of infected cities in region
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Infectious Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousIndividuals

number of infectious individuals
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number of Object Propertiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfObjectProperties

number of object properties
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number of Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfObjects

number of objects
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Occurrencesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfOccurrences

count of how many times a specific event, value, or element appears within a given context or dataset
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "e.g., number of events occurring in a fixed interval of time"@en

Number of Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfParticles

number of constituent particles in that system
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "e.g. the number of atoms in a molecule"@en

Number of Regionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfRegions

number of regions
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Removed Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedIndividuals

number of removed/recovered individuals
belongs to
Quantity c
has facts
generalized by op Removed ni
is dimensionless dp "true"^^boolean

Number Of Susceptible Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfSusceptibleCities

number of susceptible cities in region
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Number Of Susceptible Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleIndividuals

number of susceptible individuals
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment."@en

Number Of Susceptible Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfSusceptibleIndividualsFormulation

equation for the number of susceptible individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$$ \hat{\mathcal{S}}^{(l)} = \hat{\mathcal{N}}^{(l)} - (1 + \Sigma_{\mathcal{E}}) \hat{\mathcal{I}}^{(l)} - \hat{\mathcal{R}}^{(l)} $$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{N}}^{(l)}$, Total Population Size"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{R}}^{(l)}$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{S}}^{(l)}$, Number Of Susceptible Individuals"^^La Te X ep

Number of Time Pointsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfTimepoints

total number of time points at which observation were made
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Objectni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Object

anything that may be observed or acted upon by a subject
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q488383 ep

Object Cluster Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectClusterFormulation

formulation determining the coherence of object clusters
belongs to
Mathematical Formulation c
has facts
contains quantity op Object Cluster Matrix ni
contains quantity op Object Committor Functions ni
contains quantity op Object Rating Matrix ni
defining formulation dp "$\mathrm{R_c} = (\chi^T\chi)^{-1}\chi^T\mathrm{R}\chi$"^^La Te X ep
in defining formulation dp "$\chi$, Object Committor Functions"^^La Te X ep
in defining formulation dp "$\mathrm{R_c}$, Object Cluster Matrix"^^La Te X ep
in defining formulation dp "$\mathrm{R}$, Object Rating Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Object Cluster Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectClusterMatrix

matrix giving insight into the coherence of object clusters
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Object Committor Function Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommittorFunctionFormulation

formulation determining the object commitor functions
belongs to
Mathematical Formulation c
has facts
contains quantity op Object Committor Functions ni
contains quantity op Second Eigenvalue of Orthogonal Matrix ni
defining formulation dp "$\chi = [u*_2, 1 - u*_2]$"^^La Te X ep
in defining formulation dp "$\chi$, Object Committor Functions"^^La Te X ep
in defining formulation dp "$u*_2$, Second Eigenvalue of Orthogonal Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Object Committor Functionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommittorFunctions

non-negative vectors whose values correspond to the probability to end up in some property when starting the process in some object
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Object Commonality Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommonalityFormulation

function defining the entries in the object commonality matrix
belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Objects ni
contains quantity op Object ni
contains quantity op Object Commonality Matrix ni
contains quantity op Object Property ni
defining formulation dp "$M_{i,j} = f(o_i) \odot f(o_j) for i,j in N$"^^La Te X ep
in defining formulation dp "$N$, Number of Objects"^^La Te X ep
in defining formulation dp "$\mathbf{M}$,Object Commonality Matrix"^^La Te X ep
in defining formulation dp "$f(o)$, Object Property"^^La Te X ep
in defining formulation dp "$o$, Object"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Object Commonality Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommonalityMatrix

matrix containing object property commonalities of all object pairs
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Object Comparison Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectComparisonFormulation

boolean ring over object properties
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Object Comparison Model ni
contains quantity op Boolean Ring ni
contains quantity op Number of Object Properties ni
contains quantity op Object Property ni
contains quantity op Power Set ni
defining formulation dp "$\mathcal{B} = \mathcal{P}(x_1,x_2,...,x_m)$"^^La Te X ep
in defining formulation dp "$\mathcal{B}$, Boolean Ring"^^La Te X ep
in defining formulation dp "$\mathcal{P}$, Power Set"^^La Te X ep
in defining formulation dp "$m$, Number of Object Properties"^^La Te X ep
in defining formulation dp "$x$, Object Property"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Object Comparison Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectComparisonModel

mathematical model comparing objects using a boolean ring over the object properties
belongs to
Mathematical Model c
has facts
models op Identify Destruction Rules in Ancient Egyptian Objects ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Object Propertyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectProperty

property of an object
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Object Rating Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingFormulation

formulation rating the object commonalities
belongs to
Mathematical Formulation c
has facts
contains quantity op Maximal Object Descriptiveness Rating ni
contains quantity op Object Commonality Matrix ni
contains quantity op Object Rating Matrix ni
defining formulation dp "$f: \mathbf{M}\rightarrow\mathbf{R}: f(s)=y, \ s\in\mathbf{M},\ y\in\{\mathbf{R}| 0 \leq y \leq score_{max}\}$"^^La Te X ep
in defining formulation dp "$\mathbf{M}$, Object Commonality Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{R}$, Object Rating Matrix"^^La Te X ep
in defining formulation dp "$score_{max}$, Maximal Object Descriptiveness Rating"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "false"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Object Rating Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingMatrix

matrix rating the descriptiveness of the object commonalities
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Object Rating Matrix Decomposition (Schur)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingMatrixDecompositionSchur

Schur decomposition of the object rating matrix
belongs to
Mathematical Formulation c
has facts
contains quantity op Object Rating Matrix ni
contains quantity op Orthogonal Matrix ni
contains quantity op Upper-Triangular Matrix ni
defining formulation dp "$\mathbf{R} = \mathbf{U}\mathbf{V}\mathbf{U^T}$"^^La Te X ep
in defining formulation dp "$\mathbf{R}$, Object Rating Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{U}$, Orthogonal Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{V}$, Upper-Triangular Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
wikidata I D ap Q1064218 ep

Ohm Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OhmEquation

Ohm's law for transport of electric charge
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Conductivity ni
contains quantity op Electric Current Density ni
contains quantity op Electric Field ni
defining formulation dp "$J=\sigma E$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$J$, Electric Current Density"^^La Te X ep
in defining formulation dp "$\sigma$, Electric Conductivity"^^La Te X ep
description ap "Note that the formulation used here is a generalization of the well-known R=U/I."@en
wikidata I D ap Q41591 ep

Oosterhout (2024) Finite-strain poro-visco-elasticity with degenerate mobilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Oosterhout_2024_Finite-strain_poro-visco-elasticity_with_degenerate_mobility

publication
belongs to
Publication c
has facts
doi I D ap zamm.202300486 ep

Opinionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Opinion

opinion of a given individual at a given time
belongs to
Quantity c
has facts
generalizes quantity op Opinion Vector of Individuals ni
generalizes quantity op Opinion Vector of Influencers ni
generalizes quantity op Opinion Vector of Media ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q3962655 ep

Opinion Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionDynamics

modelling opinion dynamics under the impact of influencer and media strategies
belongs to
Research Problem c
has facts
contained in field op Computational Social Science ni

Opinion Model With Influencers And Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionModelWithInfluencersAndMedia

general opinion model considering individuals, traditional media and social media influencers
belongs to
Mathematical Model c
has facts
models op Opinion Dynamics ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "General opinion model resulting from a large number of individuals adapting their opinions through interaction with each other as well as due to the influence of a few specific agents with particular roles, namely traditional media and social media influencers."@en

Opinion Vector of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfIndividuals

vector containing opinions for individuals
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Opinion Vector of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfInfluencers

vector containing opinions for influencers
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Opinion Vector of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfMedia

vector containing opinions for media agents
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Optimal Controlni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControl

branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized
belongs to
Computational Task c
has facts
applies model op Control System Model (Bilinear) ni
applies model op Electron Shuttling Model ni
applies model op Quantum Model (Closed System) ni
applies model op Quantum Model (Open System) ni
contains final condition op Optimal Control Final ni
contains formulation op Optimal Control Backward ni
contains formulation op Optimal Control Forward ni
contains formulation op Optimal Control Update ni
contains initial condition op Optimal Control Initial ni
contains objective op Optimal Control Cost ni
contains objective op Optimal Control Target ni
contains output op Control System Input ni
description ap "Finding controls, e.g. external forces|fields, such that they drive a given control system from a given initial state to a specific final state (target), typically with constraints such as using not too high fields (cost)."@en
arxiv I D ap 0707.1883 ep
doi I D ap j.cpc.2018.02.022 ep
doi I D ap R01 ep
wikidata I D ap Q1971426 ep

Optimal Control Backwardni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlBackward

Lagrange multipliers of control systems are propagated backward via the adjoint of the input equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Time ni
defining formulation dp "$\dot{z}(t)=-(A^{\dagger}+ \sum_ku_k(t)N^{\dagger}_k)z(t)-B^{\dagger}u(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep

Optimal Control Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlConstraint

Constraint functional in optimal control systems requiring that the system's state vector follows the respective equation of motion
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Optimal Control ni
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$J[u,x,z]=2\Re\int_0^Tdtz^{\dagger}(t)\left(\partial_t-A-\sum_ku_k(t)N_k\right)x(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep

Optimal Control Costni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlCost

cost functional in optimal control
belongs to
Quantity c
has facts
description ap "Minimizes the cost of the control of a system, e.g. minimize the fluence of a laser field"@en

Optimal Control Cost (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlCostDefinition

cost functional in optimal control
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Optimal Control Cost ni
contains quantity op Optimal Control Penalty Factor ni
contains quantity op Time ni
defines op Optimal Control Cost ni
defining formulation dp "$J[u] \equiv \sum_k\alpha_k\int_0^Tdtu_k^2(t)$"^^La Te X ep
in defining formulation dp "$J$, Optimal Control Cost"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$\alpha$, Optimal Control Penalty Factor"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
description ap "Minimizes the cost of the control of a system, e.g. minimize the fluence of a laser field"@en

Optimal Control Finalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlFinal

final condition for the (backward) propagation of the Lagrange multiplier of a control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix D ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$z(t=T)$=Dx(t=T)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep

Optimal Control Forwardni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlForward

state vectors of control systems are propagated forward via the input equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$\dot{x}(t)=(A+ \sum_ku_k(t)N_k)x(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep

Optimal Control Initialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlInitial

initial condition for the (forward) propagation of the state vector of a control system
belongs to
Mathematical Formulation c
has facts
contains formulation op Initial Control State ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$x(t=0)=x_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$x_0$, Initial Control State"^^La Te X ep

Optimal Control Penalty Factorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlPenaltyFactor

used to balance between the two objectives: maximizing the target function[al] versus minimizing the cost function[al]
belongs to
Quantity c
has facts
description ap "In optrimal control theory, a penalty factor can be used to balance between the two objectives: maximizing the target function[al] versus minimizing the cost function[al]"@en

Optimal Control Targetni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlTarget

target functional in optimal control
belongs to
Quantity c
has facts
description ap "Maximize the quadratic output of a given control system"@en

Optimal Control Target (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlTargetDefinition

target functional in optimal control
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix D ni
contains quantity op Control System State ni
contains quantity op Optimal Control Target ni
defines op Optimal Control Target ni
defining formulation dp "$J[u,x] \equiv x^{\dagger}(T)Dx(T)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$J$, Optimal Control Target"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "Maximize the quadratic output of a given control system"@en

Optimal Control Updateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlUpdate

updated control is calculated from state vector and Lagrange multiplier of a control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Optimal Control Penalty Factor ni
contains quantity op Time ni
defining formulation dp "$u_k(t)=-\frac{1}{\alpha_k}\Im\left(z^{\dagger}(t)N_kx(t) \right)$"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$\alpha$, Optimal Control Penalty Factor"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep

Optimization in Public Transportationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimizationInPublicTransportation

using mathematical models and algorithms to improve the efficiency and effectiveness of transportation systems
belongs to
Research Field c
has facts
studied in op Gattermann (2017) Line pool generation ni

Origin Destination Datani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OriginDestinationData

data including, amongst others, information from which origin to which destination passengers travel and which mode of transport they use
belongs to
Quantity c

Orthogonal Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OrthogonalMatrix

real square matrix whose columns and rows are orthogonal unit vectors
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q333871 ep

Overall Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OverallDistributionOfIndividuals

pattern or arrangement of individuals within a population across a given area or space
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Overall Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OverallDistributionOfIndividualsFormulation

equation for the overall distribution of individuals
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Overall Distribution Of Individuals ni
defining formulation dp "$\rho = \Sigma_{m,l} \rho_{m,l}$"^^La Te X ep
in defining formulation dp "$\rho$, Overall Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep
is dimensionless dp "true"^^boolean

Pair Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PairFunction

non-negative pair function used to weight interaction between two individuals
belongs to
Quantity c
has facts
description ap "Non-negative pair function used to weight interaction between two individuals, e.g., placing exponentially more weight on close-by individuals or having interactions irrespective of the opinion distance between individuals."@en

Pair Function Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PairFunctionAssumption

pair function weighting social influence via distance in opinion space
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Opinion Model With Influencers And Media ni
contains quantity op Pair Function ni
defines op Pair Function ni
defining formulation dp "$\phi(x) = \exp(-x)$"^^La Te X ep
in defining formulation dp "$\phi(x)$, Pair Function"^^La Te X ep
is space-continuous dp "true"^^boolean

Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKinetics

determination of the kinetic constants for enzyme-catalyzed reactions
belongs to
Computational Task c
has facts
generalizes task op Linear Parameter Estimation of Enzyme Kinetics ni
generalizes task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
doi I D ap B978 0 12 801238 3.05143 6 ep

Parameter To Scale Attractive Force From Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromInfluencers

parameter to scale attractive force from influencers
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Parameter To Scale Attractive Force From Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromMedia

parameter to scale attractive force from media
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Parameter To Scale Attractive Force From Other Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromOtherIndividuals

parameter to scale attractive force from other individuals
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Partial Mean Field Opinion Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PartialMeanFieldOpinionModel

opinion model considering many individuals and few traditional media and social media influencers
belongs to
Mathematical Model c
has facts
models op Opinion Dynamics ni
description ap "For situations with many individuals but few influencers and media, one can derive the mean-field limit by a partial differential equation (PDE) that describes the opinion dynamics of individuals in the limit of infinitely many individuals but is usually already a good approximation to the dynamics for finitely many individuals. Since here the number of influencers and media is still small and finite, their dynamics are still best described by SDEs but now coupled to PDEs for the evolution of the opinion distributions of individuals."@en

Particle Flux Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticleFluxDensity

time derivative of particle fluence
belongs to
Quantity c
has facts
description ap "Particle Flux Density"@en
alt Label ap "Fluence Rate"@en
alt Label ap "Particle Fluence Rate"@en
alt Label ap "Time Derivative of Particle Fluence"@en
wikidata I D ap Q98497410 ep

Particle Number Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticleNumberDensity

number of particles per volume
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q98601569 ep

Particles In Electromagnetic Fieldsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticlesInElectroMagneticFields

motion of charged particles subject to an electric and/or magnetic fields, e.g. in a cathode ray tube, in an ion trap, or in a mass spectrometer
belongs to
Research Problem c
has facts
contained in field op Electromagnetism ni

Passive Muscle Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveMuscleForce

force developed in noncontracting or inactive muscles by the elastic elements within the muscle
belongs to
Quantity c
has facts
defined by op Passive Muscle Force (Definition) ni

Passive Muscle Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Passive_Muscle_Force

force developed in noncontracting or inactive muscles by the elastic elements within the muscle
belongs to
Mathematical Formulation c
has facts
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Muscle Length ni
contains quantity op Passive Muscle Force ni
contains quantity op Passive Muscle Strain ni
contains quantity op Stress Free Muscle Length ni
contains quantity op Time ni
defining formulation dp "$$F_{\text{PME}}(\mathcal{l}_{\text{M}}) \equiv F^\text{M}_0 \cdot \frac{\exp\left(\frac{k_{\text{PE}}}{\epsilon^{\text{M}}_0}\left(\frac{\mathcal{l_{\text{M}}(t)}}{\mathcal{l}_{\text{M}}^{\text{slack}}}-1\right)\right)-1}{\exp(k_{\text{PE}})-1}$$"^^La Te X ep
in defining formulation dp "$F^{\text{M}}_0$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PME}}$, Passive Muscle Force"^^La Te X ep
in defining formulation dp "$\epsilon^{M}_0$, Passive Muscle Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}^{\text{slack}}_{\text{M}}$, Stress Free Muscle Length"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{M}}$, Muscle Length"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Passive Muscle Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveMuscleStrain

passive muscle strain
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Strain ni

Passive Tendon Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveTendonForce

force that a tendon can generate without the muscle actively contracting
belongs to
Quantity c
has facts
defined by op Passive Tendon Force (Definition) ni
description ap "Concrete values are fitted on experimental studies, see DOI link"@en
doi I D ap ms 7 19 2016 ep

Passive Tendon Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Passive_Tendon_Force

force that a tendon can generate without the muscle actively contracting
belongs to
Mathematical Formulation c
has facts
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Passive Tendon Force ni
contains quantity op Tendon Length ni
contains quantity op Tendon Strain ni
defines op Passive Tendon Force ni
defining formulation dp "$$F_{\text{PTE}}(\mathcal{l}_{\text{T}}(t)) \equiv \begin{cases} F_0^{\text{M}} \cdot0.10377(\exp(91-\epsilon_{\text{T}}(t))-1) ~ & \text{if$\leq \epsilon_{\text{T}}(t)\leq 0.01516$ } \\ F_0^{\text{M}} \cdot (37.526 \cdot \epsilon_{\text{T}}(t) - 0.26029 ) ~ & \text{if $0.01516 <\epsilon_{\text{T}}(t) < 0.1 $} \end{cases}$$"^^La Te X ep
in defining formulation dp "$F_0^{\text{M}}$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PTE}}$, Passive Tendon Force"^^La Te X ep
in defining formulation dp "$\epsilon_{\text{T}}$, Tendon Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{T}}$, Tendon Length"^^La Te X ep

PDE SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HybridPDEODESEIRModel

spatial spreading model of susceptible, exposed, infectious, and removed individuals
belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
description ap "Spatial spreading model of SEIR(Susceptible, Exposed, Infectious, and Removed) type in a domain $\Omega \subset \mathbb{R}^2$ modeling both the SEIR dynamics and spatial diffusion of infectious individuals. Employing Partial differential equations."@en

Period Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodLength

length of a period in time units
belongs to
Quantity c
has facts
generalized by quantity op Time ni

Periodic Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodicBoundaryConditionElectricField

periodic boundary condition for electric potential, e.g., for modeling devices with repeated units
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Length Of Unit Cell ni
contains quantity op Time ni
generalized by formulation op Periodic Boundary Conditions ni
defining formulation dp "$\phi(r,t)=\phi(r+L,t)$"^^La Te X ep
in defining formulation dp "$L$, Length Of Unit Cell"^^La Te X ep
in defining formulation dp "$\phi$, Electric Potential"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Example: The SiQbus electron shuttling device contains periodically repeated unit cells with four clavier gates each."@en

Periodic Boundary Conditionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodicBoundaryConditions

set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell
belongs to
Mathematical Formulation c
has facts
description ap "When an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by one-dimensional PBCs can be thought of as being mapped onto a circle. The space made by two-dimensional PBCs can be thought of as being mapped onto a torus."@en
wikidata I D ap Q2992284 ep

Permeability (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermeabilityVacuum

strength of the magnetic field induced by an electric current
belongs to
Quantity c
has facts
description ap "The magnetic permeability in a classical vacuum. It is a physical constant that quantifies the strength of the magnetic field induced by an electric current."@en
alt Label ap "Magnetic Constant"@en
qudt I D ap Magnetic Constant ep
wikidata I D ap Q1515261 ep

Permittivity (Dielectric)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityDielectric

measure of the electric polarizability of a dielectric material
belongs to
Quantity c
has facts
description ap "In electromagnetism, the absolute permittivity, often simply called permittivity is a measure of the electric polarizability of a dielectric material. It is given as the product of the vacuum dielectric permittivity and the relative permittivity of the material. Permittivities may be complex and frequency-dependent."@en
qudt I D ap Permittivity ep
wikidata I D ap Q211569 ep

Permittivity (Relative)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityRelative

permittivity of a material expressed as a ratio with the electric permittivity of a vacuum
belongs to
Quantity c
has facts
defined by op Permittivity (Relative, Definition) ni
nondimensionalizes quantity op Permittivity (Dielectric) ni
description ap "The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivities may be complex and frequency-dependent."@en
wikidata I D ap Q4027242 ep

Permittivity (Relative, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityRelativeDefinition

permittivity of a material expressed as a ratio with the electric permittivity of a vacuum
belongs to
Mathematical Formulation c
has facts
contains quantity op Permittivity (Dielectric) ni
contains quantity op Permittivity (Relative) ni
contains quantity op Permittivity (Vacuum) ni
defining formulation dp "$\varepsilon_{\mathrm{r}} \equiv \frac{\varepsilon}{\varepsilon_0}$"^^La Te X ep
in defining formulation dp "$\varepsilon$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\varepsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\varepsilon_{\mathrm{r}}$, Permittivity (Relative)"^^La Te X ep
description ap "The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivities may be complex and frequency-dependent."@en
wikidata I D ap Q4027242 ep

Permittivity (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityVacuum

physical constant that represents the capability of the vacuum to permit electric field lines
belongs to
Quantity c
has facts
generalized by quantity op Permittivity (Dielectric) ni
description ap "Vacuum permittivity is the value of the absolute dielectric permittivity of classical vacuum. It is an ideal (baseline) physical constant."@en
alt Label ap "distributed capacitance of the vacuum"@en
alt Label ap "electric constant"@en
qudt I D ap Electric Constant ep
wikidata I D ap Q6158 ep

Physical Chemistryni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PhysicalChemistry

subdiscipline at the intersection of physics and chemistry, describing chemical concepts utilizing the principles of physics
belongs to
Research Field c
has facts
contains problem op Molecular Reaction Dynamics ni
contains problem op Molecular Spectroscopy (Transient) ni
description ap "Note that the distinction between Physical Chemistry and Chemical Physics is not always straight-forward to define."@en
mardi I D ap Item: Q133773 ep
wikidata I D ap Q11372 ep

Pi Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PiNumber

ratio of circumference and the diameter of a circle
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
alt Label ap "Archimedes' Constant"@en
wikidata I D ap Q167 ep

Planck Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PlanckConstant

quantum of action in quantum mechanics
belongs to
Quantity c
has facts
description ap "a physical constant that is the quantum of action in quantum mechanics. The Planck constant was first described as the proportionality constant between the energy of a photon and the frequency of its associated electromagnetic wave."@en
qudt I D ap Planck Constant ep
wikidata I D ap Q122894 ep

Poisson Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistribution

discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a constant mean rate of occurrence
belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
description ap "Assuming that these events occur with a known constant mean rate and independently of the time since the last event"@en
wikidata I D ap Q205692 ep

Poisson Distribution (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistributionDefinition

discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a constant mean rate of occurrence
belongs to
Mathematical Formulation c
has facts
contains quantity op Euler Number ni
contains quantity op Expectation Value ni
contains quantity op Number Of Occurrences ni
contains quantity op Poisson Distribution ni
defines op Poisson Distribution ni
defining formulation dp "$P(k;\lambda)\sim\frac{\lambda^ke^{-\lambda}}{k!}$"^^La Te X ep
in defining formulation dp "$P$, Poisson Distribution"^^La Te X ep
in defining formulation dp "$\lambda$, Expectation Value"^^La Te X ep
in defining formulation dp "$e$, Euler Number"^^La Te X ep
in defining formulation dp "$k$, Number Of Occurrences"^^La Te X ep
wikidata I D ap Q205692 ep

Poisson Equation For The Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonEquationForTheElectricPotential

For use in semiconductor physics, with electron and hole densities
belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Electrons ni
contains quantity op Density Of Holes ni
contains quantity op Doping Profile ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Permittivity (Dielectric) ni
defining formulation dp "$-\nabla\cdot\left(\epsilon_s\nabla\psi\right) = q\left(C+p(\psi,\phi_p)-n(\psi,\phi_n)\right)$"^^La Te X ep
in defining formulation dp "$C$, Doping Profile"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean

Poisson Equation For The Electric Potential (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonEquationForTheElectricPotentialFiniteVolume

Used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
contains quantity op Electric Potential ni
contains quantity op Permittivity (Dielectric) ni
discretizes formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$-\epsilon_s\left(\frac{\psi_{k+1}-\psi_{k}}{h_{k,k+1}}-\frac{\psi_{k}-\psi_{k-1}}{h_{k-1,k}}\right)=q\left(C_k+p(\psi_k,\phi_{p;k})-n(\psi_k,\phi_{n;k})\right)|\omega_k|$"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
is space-continuous dp "false"^^boolean

Poisson log-Likelihoodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonLogLikelihood

log-likelihood function of a Poisson distribution
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Death Count ni
contains quantity op Exposure Of An Individual ni
contains quantity op Likelihood Value ni
contains quantity op Risk Of Death ni
defining formulation dp "$\log L = \sum_{x}[D(x)\log\mu(x)-E(x)\mu(x)]$"^^La Te X ep
in defining formulation dp "$D$, Death Count"^^La Te X ep
in defining formulation dp "$E$, Exposure Of An Individual"^^La Te X ep
in defining formulation dp "$L$, Likelihood Value"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep

Poisson-Distributed Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistributedDeaths

Assuming that death counts at age x are Poisson-distributed
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Death Count ni
contains quantity op Exposure Of An Individual ni
contains quantity op Poisson Distribution ni
contains quantity op Risk Of Death ni
defining formulation dp "$D(x)\sim P\left(E(x)\mu(x)\right)$"^^La Te X ep
in defining formulation dp "$D$, Death Count"^^La Te X ep
in defining formulation dp "$E$, Exposure Of An Individual"^^La Te X ep
in defining formulation dp "$P$, Poisson Distribution"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep

Polar Angleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PolarAngle

angle in the spherical coordinate system
belongs to
Quantity Kind c
has facts
wikidata I D ap Q116757614 ep

Pomologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Pomology

branch of botany that studies fruits and their cultivation
belongs to
Research Field c
has facts
contains problem op Gravitational Effects On Fruit ni
generalized by field op Biology ni
wikidata I D ap Q35911 ep

Population Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PopulationDensity

measure of the number of individuals per unit area
belongs to
Quantity c
has facts
description ap "Population density is a measure of the number of individuals per unit area, typically expressed as the number of individuals per square kilometer. It is used to study human and animal populations for various administrative and scientific purposes."@en

Poro-Visco-Elastic (Dirichlet Boundary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDirichletBoundary

Dirichlet boundary condition for mechanical deformation
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Poro-Visco-Elastic Model ni
contains quantity op Mechanical Deformation ni
contains quantity op Mechanical Deformation (Boundary Value) ni
contains quantity op Spatial Variable ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\chi(t,x) = \chi_D(t,x)$"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\chi_D$, Mechanical Deformation (Boundary Value)"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep

Poro-Visco-Elastic (Neumann Boundary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticNeumannBoundary

Neumann boundary condition for mechanical deformation
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Poro-Visco-Elastic Model ni
contains quantity op Concentration ni
contains quantity op Free Energy Density ni
contains quantity op Mechanical Deformation ni
contains quantity op Spatial Variable ni
contains quantity op Surface Force Density ni
contains quantity op Unit Normal Vector ni
contains quantity op Viscous Dissipation Potential ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$(\partial_{\nabla \chi} \Phi(x,\nabla\chi(t,x),c(t,x)) + \partial_{\nabla\dot\chi}\zeta(x,\nabla\dot\chi(t,x),\nabla\chi(t,x),c(t,x)))\nu - \nabla_s\cdot (\partial_{D^2\chi} H(x,D^2\chi(t,x))\nu) = g(t,x)$"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\nu$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$\zeta$, Viscous Dissipation Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$g$, Surface Force Density"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep

Poro-Visco-Elastic Diffusion Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDiffusionBoundaryCondition

Boundary condition for diffusion equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op External Chemical Potential ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Hydraulic Conductivity ni
contains quantity op Mechanical Deformation ni
defining formulation dp "$M(\nabla\chi,c)\nabla\partial_c\Phi(x,\nabla\chi,c)\cdot \nu = \kappa(x)(\mu_e(t,x)-\partial_c\Phi(x,\nabla\chi,c))$"^^La Te X ep
in defining formulation dp "$M$, Hydraulic Conductivity"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\kappa$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\mu$, External Chemical Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep

Poro-Visco-Elastic Diffusion Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDiffusionEquation

mathematical formulation for diffusion in poro-visco-elastic models
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Free Energy Density ni
contains quantity op Hydraulic Conductivity ni
contains quantity op Mechanical Deformation ni
contains quantity op Time ni
generalizes formulation op Fick Equation ni
defining formulation dp "$\dot c(t,x) = - \nabla\cdot(M(x,\nabla\chi(t,x),c(t,x))\nabla\partial_c\Phi(x,\nabla \chi(t,x),c(t,x)))$"^^La Te X ep
in defining formulation dp "$M$, Hydraulic Conductivity"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Poro-Visco-Elastic Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticEvolution

simulation of coupled mechanical deformation of solids to other physical processes such as heat conduction or diffusion of chemical species
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
description ap "This is relevant in many applications in thermo-mechanics, solid-state batteries, poroelasticity in biological tissue, hydrogen storage, and elastomeric materials."@en
doi I D ap zamm.202300486 ep

Poro-Visco-Elastic Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticModel

mathematical model describing the coupled evolution of the mechanical deformation and the concentration of a species
belongs to
Mathematical Model c
has facts
models op Poro-Visco-Elastic Evolution ni
is deterministic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "The elastic stresses are given via the derivative of a free energy density function, the viscous stresses are of Kelvin-Voigt type and formulated in terms of a dissipation potental. The evolution of the concentration is given via a diffusion equation that is pulled-back to the reference configuration. The mobility law depends nonlinearly on the deformation gradient and the concentration itself."@en
description ap "The finite mechanical deformation is quasistatic and is formulated in the Lagrangian frame. The total stress consists of elastic and viscous stresses. Moreover, a second-order hyper-stress regularization is taken into account."@en
doi I D ap zamm.202300486 ep

Poro-Visco-Elastic Quasistatic Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticQuasistaticEquation

equation using linear momentum without inertia for mechanical deformation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Poro-Visco-Elastic Model ni
contains quantity op Concentration ni
contains quantity op External Force Density ni
contains quantity op Free Energy Density ni
contains quantity op Hyperstress Potential ni
contains quantity op Mechanical Deformation ni
contains quantity op Spatial Variable ni
contains quantity op Time ni
contains quantity op Viscous Dissipation Potential ni
defining formulation dp "$-\nabla\cdot(\partial_{\nabla \chi} \Phi(x,\nabla\chi(t,x),c(t,x)) + \partial_{\nabla\dot\chi}\zeta(x,\nabla\dot\chi(t,x),\nabla\chi(t,x),c(t,x)) - \nabla\cdot \partial_{D^2\chi} H(x,D^2\chi(t,x)))=f(t,x)$"^^La Te X ep
in defining formulation dp "$H$, Hyperstress Potential"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\zeta$, Viscous Dissipation Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$f$, External Force Density"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep

Power Setni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PowerSet

mathematical set containing all subsets of a given set
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q205170 ep

Pressureni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Pressure

force applied over an area
belongs to
Quantity Kind c
has facts
qudt I D ap Pressure ep
wikidata I D ap Q39552 ep

Probability Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProbabilityDistribution

statistical function that describes the likelihood of obtaining all possible values that a random variable can take
belongs to
Quantity c
has facts
description ap "mathematical function that describes the probability of occurrence of different possible outcomes in a (real world or statistical computer) experiment"@en
alt Label ap "Probability Density"@en
wikidata I D ap Q200726 ep

Product 1 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1Concentration

amount of product 1 present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{5} c_{EP_1} - k_{-5} c_{E} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{5} c_{EP_1} - k_{-5} c_{E} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{2} c_{ES_1} - k_{-2} c_{E*} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{2} c_{ES_1} c_{S_2} - k_{-2} c_{EP_2} c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 2 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2Concentration

amount of product 2 present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-4} c_{EP_1} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} c_{EP_{1}P_{2}} - k_{-4} c_{EP_1} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} c_{E*S_2} - k_{-4} c_{P_2} c_{E}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{3} c_{EP_2} - k_{-3} c_{E} c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Product Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProductConcentration

amount of product present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Product Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProductConcentrationODEUniUni

ordinary differential equation describing the concentration over time in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P}}{dt}=k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Proton Electron Mass Rationi back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProtonElectronMassRatio

proton-to-electron mass ratio
belongs to
Quantity Kind c
has facts
nondimensionalizes quantity op Proton Mass ni
is dimensionless dp "true"^^boolean
qudt I D ap Value Proton Electron Mass Ratio ep
wikidata I D ap Q2912520 ep

Proton Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProtonMass

fundamental physical constant giving the proton rest mass
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
qudt I D ap Proton Mass ep
wikidata I D ap Q97275155 ep

PTN Lineni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PTNLine

single line in a public transport network (PTN)
belongs to
Quantity c
has facts
wikidata I D ap "https://www.wikidata.org/wiki/Q125209036"

Public Transportation Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PublicTransportationNetwork

graph given by a set of stops or stations and a set of direct connections between them
belongs to
Mathematical Formulation c
has facts
contains quantity op Edges ni
contains quantity op Nodes ni
studied in op Gattermann (2017) Line pool generation ni
defining formulation dp "$PTN=(V,E)$"^^La Te X ep
in defining formulation dp "$E$, Edges"^^La Te X ep
in defining formulation dp "$V$, Nodes"^^La Te X ep
wikidata I D ap Q18325841 ep

Quantile Function Of The Beta Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantileFunctionOfTheBetaDistribution

inverse function of the regularized incomplete beta function
belongs to
Quantity c
has facts
wikidata I D ap Q3489473 ep
wikidata I D ap Q756254 ep

Quantum Angular Momentum Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumAngularMomentumOperator

quantum mechanical operator related to rotational symmetry
belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
description ap "In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry."@en
wikidata I D ap Q1190143 ep

Quantum Classical Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumClassicalModel

hybrid quantum-classical model for a system with fast and slow degrees of freedom
belongs to
Mathematical Model c
has facts
contains formulation op Schrödinger-Newton Equation ni
contains initial condition op Initial Classical Momentum ni
contains initial condition op Initial Classical Position ni
contains initial condition op Initial Quantum State ni
contains model op Classical Dynamics Model ni
contains model op Quantum Model (Closed System) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Typically used for a system comprising of light/fast and heavy/slow particles where the classical approximation can be only justified for the latter ones"@en

Quantum Conditional Quasi-Solvabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumConditionalQuasiSolvability

exact solutions of the time-independent Schrödinger equation for a certain number of low-lying states if certain relations of the parameters hold
belongs to
Computational Task c
has facts
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
contains formulation op Schrödinger Equation (Time Independent) ni
contains input op Rotational Constant ni
contains output op Electric Field ni
contains output op Quantum Eigen Energy ni
contains output op Quantum State Vector (Stationary) ni
description ap "For certain Hamiltonians, the concept of Conditional Quasi-Solvability holds: There are exact solutions of the time-independent Schrödinger equation for a certain number of low-lying quantum states (quasi-exact solvability), if and only if certain relations of the parameters of the Hamiltonian hold (conditionally exact solvability). For examples with trigonometric and hyperbolic potentials, see the annotating DOIs."@en
doi I D ap 1.4864465 ep
doi I D ap Phys Rev. A.91.022111 ep
doi I D ap Phys Rev A.97.053417 ep
doi I D ap e2017 80134 6 ep
doi I D ap fphy.2014.00037 ep

Quantum Damping Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumDampingRate

rate at which quantum coherence is lost in a system due to interactions with its environment
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate Constant ni
description ap "Quantum damping rates can be used - together with quantum jump operators - to describe the dissipation and/or decoherence of the quantum dynamics in a Lindblad equation (for open quantum systems)"@en
alt Label ap "Dissipative Transition Rate"@en

Quantum Density Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumDensityOperator

matrix that describes an ensemble of physical systems as quantum states
belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
generalizes quantity op Quantum State Vector ni

Quantum Eigen Energyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergy

specific, quantized energy levels that a quantum system can possess
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Independent) ni
description ap "Eigenenergy are obtained as eigenvalues of the Quantum Hamiltonian Operator by solving the time-independent Schrödinger equation."@en
wikidata I D ap Q190524 ep
wikidata I D ap Q230883 ep

Quantum Eigen Energy (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyAnharmonic

Eigenenergies of anharmonic oscillator systems, e.g. molecular vibrations, beyond the harmonic approximation
belongs to
Mathematical Formulation c
has facts
contains quantity op Anharmonicity Constant ni
contains quantity op Number of Particles ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$E_n=\sum_{r=1}^{3N-6}\omega_k\left( n_r + \frac{1}{2} \right) +\sum_{r \gt s} \chi_{rs} k\left( n_r + \frac{1}{2} \right) k\left( n_s + \frac{1}{2} \right)$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\chi$, Anharmonicity Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
wikidata I D ap Q545228 ep

Quantum Eigen Energy (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyHarmonic

Eigenenergies of (single or coupled, for N particles) harmonic oscillators, e.g. molecular vibrations, within the harmonic approximation
belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Particles ni
contains quantity op Planck Constant ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Eigen Energy (Anharmonic) ni
defining formulation dp "$E_n=\sum_{k=1}^{3N-6}\left( n_k + \frac{1}{2} \right) \hbar \omega_k$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
wikidata I D ap Q677864 ep

Quantum Eigen Energy (Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyIntermolecular

Eigenenergies of molecular vibrations, including the effects of intermolecular vibrations
belongs to
Mathematical Formulation c
has facts
contains formulation op Vibrational Frequency Shift (1st Order) ni
contains formulation op Vibrational Frequency Shift (2nd Order) ni
description ap "For simplicity, here only for a chromophore interacting with solvent molecules of a different species. Hence, only non-degenerate perturbation theory (up to 2nd order) is used here. First and second order results for the 0->1 vibrational frequency|energy shifts are given as two separate formulations."@en

Quantum Hamiltonian (Electric Charge)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricCharge

quantum-mechanical Hamiltonian for a particle with an electric charge interacting with external electric fields
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contains quantity op Electric Charge ni
contains quantity op Electric Potential ni
contains quantity op Quantum Hamiltonian Operator ni
generalizes formulation op Quantum Hamiltonian (Electric Dipole) ni
defining formulation dp "$H=H_0+q \mathcal{E}$"^^La Te X ep
in defining formulation dp "$H_0$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Potential"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep

Quantum Hamiltonian (Electric Dipole)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricDipole

Quantum-mechanical Hamiltonian for a system interacting (resonantly) through its permanent dipole moments with external electric fields
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contains quantity op Electric Dipole Moment ni
contains quantity op Electric Field ni
contains quantity op Quantum Hamiltonian Operator ni
defining formulation dp "$H=H_0-\mu \cdot \mathcal{E}$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$H_0$, Quantum Hamiltonian Operator (non-interacting system)"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Field"^^La Te X ep
in defining formulation dp "$\mu$, Electric Dipole Moment"^^La Te X ep
description ap "Semiclassical first order approximation"@en

Quantum Hamiltonian (Electric Polarizability)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricPolarizability

Quantum-mechanical Hamiltonian for a system interacting (non-resonantly) through its induced dipole moments with external electric fields
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Quantum Model (Closed System) ni
contained as formulation in op Quantum Model (Open System) ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contained as formulation in op Schrödinger Equation (Time Independent) ni
contains quantity op Electric Field ni
contains quantity op Electric Polarizability ni
contains quantity op Quantum Hamiltonian Operator ni
defining formulation dp "$H=H_0 - \frac{1}{2} \alpha \mathcal{E}^2$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$H_0$, Hamiltonian Operator (non-interacting system)"^^La Te X ep
in defining formulation dp "$\alpha$, Electric Polarizability"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Field"^^La Te X ep
description ap "Semiclassical second order approximation"@en

Quantum Hamiltonian (Linear Rotor)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianLinearRotor

quantum-mechanical represention of a molecule as a linear rotor
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Rotational Constant ni
generalized by formulation op Quantum Hamiltonian (Non-Rigid Rotor) ni
defining formulation dp "$E_j=Bj(j+1)$"^^La Te X ep
defining formulation dp "$\hat{H}=B\hat{J}^2$"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$J$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$j$, Quantum Number"^^La Te X ep
wikidata I D ap Q2915184 ep
wikidata I D ap Q904380 ep

Quantum Hamiltonian (Non-Rigid Rotor)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNonRigidRotor

quantum-mechanical represention of a molecule as a non-rigid rotor
belongs to
Mathematical Formulation c
has facts
contains quantity op Centrifugal Distortion Constant ni
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Rotational Constant ni
defining formulation dp "$E_j=Bj(j+1)-Dj^2(j+1)^2$"^^La Te X ep
defining formulation dp "$\hat{H}=B\hat{J}^2+D\hat{J}^4$"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$D$, Centrifugal Distortion Constant"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$J$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$j$, Quantum Number"^^La Te X ep
wikidata I D ap Q2915184 ep
wikidata I D ap Q904380 ep

Quantum Hamiltonian (Normal Mode)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalMode

quantum-mechanical represention of molecular vibrations in terms of normal modes
belongs to
Mathematical Formulation c
has facts
description ap "pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation"@en
wikidata I D ap Q900488 ep

Quantum Hamiltonian (Normal Mode, Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeAnharmonic

quantum-mechanical represention of molecular normal modes of vibration beyond the harmonic approximation
belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Hamiltonian (Normal Mode) ni
defining formulation dp "$\hat{H}=\frac{1/2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right) + \frac{1}{6} \sum_{ijk} \phi_{ijk} q_iq_jq_k + \frac{1}{24} \sum_{ijkl} \phi_{ijk} q_iq_jq_kq_l$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi_{ijkl}$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$\phi_{ijk}$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep

Quantum Hamiltonian (Normal Mode, Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeHarmonic

quantum-mechanical represention of molecular normal modes of vibration within the harmonic approximation
belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
defining formulation dp "$\hat{H}=\frac{1/2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right)$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep

Quantum Hamiltonian (Normal Mode, Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeIntermolecular

quantum-mechanical represention of molecular normal modes of vibration, including intermolecular interaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate ni
contains quantity op Normal Mode Momentum ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalizes formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
defining formulation dp "$\hat{H}=\frac{1}{2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right) + \frac{1}{6} \sum_{ijk} \phi_{ijk} q_iq_jq_k + \frac{1}{24} \sum_{ijkl} \phi_{ijk} q_iq_jq_kq_l + U(q)$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate"^^La Te X ep

Quantum Hamiltonian (Symmetric Top)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianSymmetricTop

quantum-mechanical represention of a molecule as a symmetric top
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Conditional Quasi-Solvability ni
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Rotational Constant ni
generalizes formulation op Quantum Hamiltonian (Linear Rotor) ni
defining formulation dp "$\hat{H}=A\hat{J_A}^2 + B\hat{J_B}^2 + C\hat{J_C}^2$"^^La Te X ep
in defining formulation dp "$A$, Rotational Constant"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$C$, Rotational Constant"^^La Te X ep
in defining formulation dp "$J_A$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$J_B$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$J_C$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
description ap "A symmetric top is a molecule in which two moments of inertia are the same. By definition a symmetric top must have a 3-fold or higher order rotation axis. In practice, spectroscopists divide molecules into two classes of symmetric tops: Oblate symmetric tops (saucer or disc shaped), e.g., C6H6, and Prolate symmetric tops (rugby football, or cigar shaped), e.g. CH3Cl."@en
wikidata I D ap Q904380 ep

Quantum Hamiltonian Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianOperator

operator representing the total energy of a quantum system
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Dependent) ni
contained in formulation op Schrödinger Equation (Time Independent) ni
generalizes quantity op Classical Hamilton Function ni
description ap "In quantum mechanics, this is the operator representing the total energy of a quantum system, thus giving the possible outcomes of energy measurements as well as its time evolution"@en
description ap "Operator in der Quantenmechanik, der (mögliche) Energiemesswerte und die Zeitentwicklung angibt."@de
wikidata I D ap Q660488 ep

Quantum Jump Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumJumpOperator

operators describing the dissipation and/or decoherence of open system quantum dynamics in a Lindblad equation
belongs to
Quantity c
has facts
defined by op Quantum Jump Operator (Definition) ni
generalized by quantity op Quantum Mechanical Operator ni
description ap "Quantum jump operators can be used - together with quantum damping rates - to describe the dissipation and/or decoherence of the quantum dynamics in a Lindblad equation (for open quantum systems)"@en
alt Label ap "Lindblad Operator"@en

Quantum Jump Operator (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumJumpOperatorDefinition

Together with quantum damping rates, these operators describe the dissipation and/or decoherence of open system quantum dynamics in a Lindblad equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Jump Operator ni
defining formulation dp "$\hat{C_{j,k}} \equiv \sqrt{\Gamma_{k\rightarrow k}}|j\rangle\langle k|$"^^La Te X ep
in defining formulation dp "$\Gamma$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$\hat{C}$, Quantum Jump Operator"^^La Te X ep
description ap "operators describing the dissipation and/or decoherence of open system quantum dynamics in a Lindblad equation"@en

Quantum Kinetic Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumKineticOperator

operator representing the kinetic energy of a quantum system
belongs to
Quantity c
has facts
description ap "In quantum mechanics, this is the operator representing the kinetic energy of a quantum system. Typically, a function of the momenta of the particles. Hence, a derivative operator"@en

Quantum Lindblad Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumLindbladEquation

describes open system quantum dynamics including dissipation and/or decoherence
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Model (Open System) ni
contains initial condition op Initial Quantum Density ni
contains quantity op Planck Constant ni
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Jump Operator ni
contains quantity op Time ni
defining formulation dp "$\frac{\mathrm d}{\mathrm{d}t}\rho=-\frac{\mathrm i}\hbar[H,\rho]+\sum _{i=1}^{N^2-1}\gamma_i\left(L_i\rho L_i^\dagger-\frac12[L_i^\dagger L_i,\rho]_+\right)$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$L$, Quantum Jump Operator"^^La Te X ep
in defining formulation dp "$[\cdot,\cdot]_+$, anti-commutator"^^La Te X ep
in defining formulation dp "$\gamma > 0$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "true"^^boolean
description ap "Markovian quantum master equation for the evolution of quantum mechanical density matrices (pure or mixed states). It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics is no longer unitary, but still satisfies the property of being trace-preserving and completely positive for any initial condition"@en
alt Label ap "Gorini–Kossakowski–Sudarshan–Lindblad Equation"@en
wikidata I D ap Q4476520 ep

Quantum Mechanical Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMechanicalOperator

mathematical construct that corresponds to a physical observable, such as position, momentum, or energy
belongs to
Quantity c
has facts
generalizes quantity op Quantum Density Operator ni
generalizes quantity op Quantum Hamiltonian Operator ni
generalizes quantity op Quantum Kinetic Operator ni
generalizes quantity op Quantum Potential Operator ni

Quantum Model (Closed System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumModelClosedSystem

quantum dynamics of a closed system, i.e., a system that is not interacting with its environment
belongs to
Mathematical Model c
has facts
contains formulation op Schrödinger Equation (Time Dependent) ni
contains initial condition op Initial Quantum Density ni
contains initial condition op Initial Quantum State ni
generalizes model op Classical Dynamics Model ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "A famous example is Schrödinger's cat, but only as long as the box is not opened!"@en

Quantum Model (Open System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumModelOpenSystem

quantum dynamics of an open system, i.e., a system that interacts with its environment
belongs to
Mathematical Model c
has facts
applied by task op Balanced Truncation (Bi-linear) ni
applied by task op H2 Optimal Approximation (Bi-linear) ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains initial condition op Initial Quantum Density ni
generalizes model op Quantum Model (Closed System) ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Quantum dynamics of an open system, i.e., a system that can exchange phase (e.g. in elastic collisions) and/or energy (e.g. in inelastic collisions) with its environment."@en

Quantum Momentum Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMomentumOperator

in the coordinate representation of quantum mechanics, the momentum of a particle is represented by this operator
belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
wikidata I D ap Q692457 ep

Quantum Momentum Operator (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMomentumOperatorDefinition

in the coordinate representation of quantum mechanics, the momentum of a particle is represented by this operator
belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Momentum Operator ni
defines op Quantum Momentum Operator ni
defining formulation dp "$p\equiv-{\rm i}\hbar \nabla$"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$p$, Quantum Momentum Operator"^^La Te X ep
wikidata I D ap Q692457 ep

Quantum Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumNumber

quantities that characterize the possible states of the system
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Independent) ni
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics."@en
wikidata I D ap Q232431 ep

Quantum Potential Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumPotentialOperator

operator representing the potential energy of a quantum system
belongs to
Quantity c
has facts
description ap "In quantum mechanics, this is the operator representing the potential energy of a quantum system. Typically, a function of the positions of the particles. Hence, a multiplicative operator"@en

Quantum State Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVector

state of an isolated quantum system, represented as an element of a projective Hilbert space
belongs to
Quantity c
has facts
description ap "Abstract (Dirac) notation as a quantum state or wave function in coordinate representation"@en
wikidata I D ap Q230883 ep

Quantum State Vector (Dynamic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVectorDynamic

solutions of the time-dependent Schrödinger equation, giving the time evolution of a (closed) quantum system
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Dependent) ni
generalized by quantity op Quantum State Vector ni
description ap "Abstract (Dirac) notation as dynamic quantum states or wave functions in coordinate representation"@en

Quantum State Vector (Stationary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVectorStationary

solutions of the time-independent Schrödinger equation, giving stationary states of a (closed) quantum system
belongs to
Quantity c
has facts
generalized by quantity op Quantum State Vector ni
description ap "Abstract (Dirac) notation as stationary quantum states or wave functions in coordinate representation."@en

Radiusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Radius

segment in a circle or sphere from its center to its perimeter or surface and its length
belongs to
Quantity Kind c
has facts
wikidata I D ap Q173817 ep

Rapid Equilibrium Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RapidEquilibriumAssumption

catalytic rate constant mich lower than unbinding rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Reaction Rate Constant ni
defining formulation dp "$k_{catalytic} \ll k_{unbind}$"^^La Te X ep
in defining formulation dp "$k_{catalytic}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{unbind}$, Reaction Rate Constant"^^La Te X ep

Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Rate

quantity of process intensivity
belongs to
Quantity Kind c
has facts
generalizes quantity op Rate Of Aging ni
generalizes quantity op Reaction Rate ni
generalizes quantity op Risk Of Death ni
description ap "Rate"@de
wikidata I D ap Q1144560 ep

Rate Of Agingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfAging

speed at which an individual or population ages
belongs to
Quantity c

Rate Of Becoming Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfBecomingInfectious

inverse of Incubation period
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Rate Of Change Of Population Density Fraction Of Exposed PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfExposedPDE

partial derivative of population density fraction of exposed
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Asymptomatic Infection Rate ni
contains quantity op Asymptomatic Recovery Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Population Density ni
contains quantity op Rate Of Becoming Infectious ni
contains quantity op Symptomatic Infection Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t e =\operatorname{div}(D \nabla e)+\left(1-\frac{A}{n+n_0}\right) s\left(\beta_e e+\beta_i i\right)-\sigma e-\phi_e e $"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\beta_e$, Asymptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\beta_i$, Symptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\phi_e$, Asymptomatic Recovery Rate"^^La Te X ep
in defining formulation dp "$\sigma$, Rate Of Becoming Infectious"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Infectious PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfInfectiousPDE

partial derivative of population density fraction of infectious
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Infected Recovery Rate ni
contains quantity op Rate Of Becoming Infectious ni
contains quantity op Time ni
defining formulation dp "$\partial_t i =\operatorname{div}(D \nabla i)+\sigma e-\phi_i i $"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\phi_i$, Infected Recovery Rate"^^La Te X ep
in defining formulation dp "$\sigma$, Rate Of Becoming Infectious"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Removed PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfRemovedPDE

partial derivative of population density fraction of removed
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Asymptomatic Recovery Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Infected Recovery Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t r =\operatorname{div}(D \nabla r)+\phi_i i+\phi_e e $"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\phi_e$, Asymptomatic Recovery Rate"^^La Te X ep
in defining formulation dp "$\phi_i$, Infected Recovery Rate"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Susceptibles PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfSusceptiblesPDE

partial derivative of population density fraction of susceptibles
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Asymptomatic Infection Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Population Density ni
contains quantity op Symptomatic Infection Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t s =\operatorname{div}(D \nabla s)-\left(1-\frac{A}{n+n_0}\right) s\left(\beta_e e+\beta_i i\right)$"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\beta_e$, Asymptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\beta_i$, Symptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Susceptible Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfSusceptibleCities

rate of change of susceptible cities
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Rate Of Switching Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfSwitchingInfluencers

rate at which an individual switches the influencer they are following at a given time
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Rate Of Switching Influencers Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfSwitchingInfluencersFormulation

rate of switching influencers
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Link Recommendation Function ni
contains quantity op Medium Influencer Fraction ni
contains quantity op Opinion ni
contains quantity op Pair Function ni
contains quantity op Rate Of Switching Influencers ni
contains quantity op Scaling Parameter For Switching Influencers ni
contains quantity op Time ni
defining formulation dp "$\Lambda_m^{\rightarrow l}(x, t)=\eta \psi\left(\left\|z_l-x\right\|\right) r\left(\frac{n_{m, l}(t)}{\sum_{m^{\prime}=1}^M n_{m^{\prime}, l}(t)}\right)$"^^La Te X ep
in defining formulation dp "$\Lambda_m^{\rightarrow l}(x, t)$, Rate Of Switching Influencers"^^La Te X ep
in defining formulation dp "$\eta$, Scaling Parameter For Switching Influencers"^^La Te X ep
in defining formulation dp "$\psi$, Pair Function"^^La Te X ep
in defining formulation dp "$n_{m, l}$, Medium Influencer Fraction"^^La Te X ep
in defining formulation dp "$r$, Link Recommendation Function"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
is space-continuous dp "true"^^boolean
description ap "Each individual i can at any time t switch its current influencer l′ to another influencer l with a given rate. By setting the pair function to $\psi(x) = exp(−x)$, an individual has an exponentially higher rate to switch to an influencer that has a similar opinion than to an influencer with a very different opinion. This rate of switching influencers is defined by this formulation."@en

Reaction Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRate

speed at which a chemical reaction proceeds
belongs to
Quantity c
has facts
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateConstant

quantifies the rate of a chemical reaction
belongs to
Quantity c
has facts
is dimensionless dp "false"^^boolean
wikidata I D ap Q658700 ep

Reaction Rate of Enzymeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzyme

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 1 - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct1Product2Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 1 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct1Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct2Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateofEnzymeSubstrate1Substrate2EnzymeProduct1Product2Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeSubstrate1Substrate2Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeSubstrate1Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Intermediateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfIntermediate

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Intermediate - Substrate 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfIntermediateSubstrate2Complex

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfProduct1

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfProduct2

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Substrate 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfSubstrate1

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Reaction Rate of Substrate 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfSubstrate2

reaction rate of specific entity
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
wikidata I D ap Q3394849 ep

Real Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RealDimensionless

quantity along a continuous line
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q12916 ep

Reciprocal Latticeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReciprocalLattice

mathematical construct to describe the diffraction patterns of crystals
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni
description ap "In solid state physics, the reciprocal lattice emerges from the Fourier transform of the direct lattice which is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which refers to the wavevector."@en
wikidata I D ap Q164129 ep

Reciprocal Lattice Vectorsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReciprocalLatticeVectors

mathematical constructs used in the study of periodic structures
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni
description ap "In solid state physics, the reciprocal lattice emerges from the Fourier transform of the direct lattice which is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which refers to the wavevector."@en
wikidata I D ap Q164129 ep

Recombination Of Electron Hole Pairsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RecombinationOfElectronHolePairs

combined effect of recombination and generation of electron-hole pairs
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate Constant ni
description ap "For use in semiconductor physics; strictly speaking, the combined effect of recombination and generation of electron-hole pairs"@en

Recurrent Neural Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Recurrent_Neural_Network

class of artificial neural network where connections between units form a directed graph along a temporal sequence
belongs to
Mathematical Model c
has facts
generalizes model op Recurrent Neural Network Surrogate for Discrete Element Method ni
wikidata I D ap Q1457734 ep

Recurrent Neural Network Surrogate for Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Recurrent_Neural_Network_Surrogate_for_Discrete_Element_Method

surrogate model employing recurrent neural networks to approximate discrete element method simulations
belongs to
Mathematical Model c
has facts
models op Efficient Numerical Simulation of Soil-Tool Interaction ni
studied in op Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni

Regionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Region

area of land that shares common features, which can be either natural or artificial
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q82794 ep

Region Connectivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RegionConnectivity

connectivity between regions
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Relative Removal Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativeRemovalRate

probability that one infective will be removed from the infection process during a unit time interval
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "true"^^boolean

Relativistic Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativisticMomentum

momentum of a particle in special relativity
belongs to
Quantity c
has facts
defined by op Relativistic Momentum (Definition) ni
generalized by quantity op Momentum ni

Relativistic Momentum (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativisticMomentumDefinition

momentum of a particle in special relativity
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Mass ni
contains quantity op Relativistic Momentum ni
contains quantity op Speed Of Light ni
defining formulation dp "$p\equiv\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$"^^La Te X ep
in defining formulation dp "$c$, Speed Of Light"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Relativistic Momentum"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep

Removedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Removed

general quantity for removed entities
belongs to
Quantity c
has facts
generalized by op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
alt Label ap "Recovered"@en
alt Label ap "Resistant"@en

Removed At Time Step n+1 in the Discrete SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheSIRModel

equation for removed individuals in the SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
discretizes op Continuous Rate of Change of Removed in the SIR Model ni
defining formulation dp "$R_{n+1} = R_n + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Removed At Time Step n+1 in the Discrete SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheSIRModelWithBirthsAndDeaths

equation for removed individuals in the discrete SIR Model with births and deaths
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
defining formulation dp "$R_{n+1} = R_n(1 - \beta \Delta t) + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Removed At Time Step n+1 in The Multi-Population Discrete SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheMultiPopulationSIRModel

equation for removed individuals in the discrete multi-population SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
defining formulation dp "$R_{n+1}^i = R_n^i + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n^i$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Risk Of Deathni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RiskOfDeath

risk (or hazard) of death, at a certain age
belongs to
Quantity c
has facts
qudt I D ap Incidence Rate ep

Roman Archaeologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanArchaeology

archaeological sub-discipline
belongs to
Research Field c
has facts
generalized by field op Archaeology ni
wikidata I D ap Q44097629 ep

Romanization Parameter Estimationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationParameterEstimation

given a set of data points the contact network and time-dependent spreading rate are determined
belongs to
Computational Task c
has facts
applies model op Susceptible Infectious Epidemic Spreading Model ni
contains constraint condition op Contact Network Constraint ni
contains constraint condition op Spreading Rate (Time-dependent) Constraint ni
contains formulation op Loss Function Minimization ni
contains input op Spreading Curve (Approximate) ni
contains input op Romanized Cities Vector ni
contains output op Contact Network (Time-dependent) ni

Romanization Spreading in Northern Tunesiani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationSpreadingInNorthernTunesia

understanding the mechanisms and dynamics of Romanization spreading in Northern Tunisia
belongs to
Research Problem c
has facts
contained in field op Roman Archaeology ni
description ap "Understanding the mechanisms and dynamics of Romanization spreading in Northern Tunisia from 146 BC to 350 AD based on sparse and fragmented archaeological data."@en

Romanization Time Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationTimeEvolution

given a set of initially infected cities, a contact network, and a time-dependent spreading rate, the spreading curve for the romanization is calculated
belongs to
Computational Task c
has facts
applies model op Susceptible Infectious Epidemic Spreading Model ni
contains formulation op Susceptible Infectious Epidemic Spreading ODE System ni
contains input op Number Of Susceptible Cities ni
contains output op Spreading Curve (Approximate) ni
contains output op Number Of Susceptible Cities ni
contains parameter op Contact Network ni
contains parameter op Spreading Rate (Time-dependent) ni

Romanized Cities Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizedCitiesVector

observed number of romanized cities
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Rotational Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RotationalConstant

scale of rotational energies in molecular spectroscopy
belongs to
Quantity c
has facts
description ap "In rotational spectroscopy, the energy levels of a molecule are often given in terms of its rotational constant"@en
wikidata I D ap Q904380 ep

Runge–Kutta Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RungeKuttaMethod

family of implicit and explicit methods used in temporal discretization for the approximate solutions of differential equations
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Euler Backward Method ni
generalizes formulation op Euler Forward Method ni
defining formulation dp "$\begin{array}{c|cccc} c_1 & a_{11} & a_{12}& \dots & a_{1s}\\c_2 & a_{21} & a_{22}& \dots & a_{2s}\\ \vdots & \vdots & \vdots& \ddots& \vdots\\c_s & a_{s1} & a_{s2}& \dots & a_{ss} \\\hline & b_1 & b_2 & \dots & b_s\\ \end{array}$"^^La Te X ep
description ap "These methods, which include the Euler method, were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta."@en
wikidata I D ap Q725944 ep

Scaling Parameter For Switching Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ScalingParameterForSwitchingInfluencers

scaling parameter used in the rate of switching influencers
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Scharfetter-Gummel Schemeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ScharfetterGummelScheme

finite volume disretization scheme for solving the van Roosbroeck system describing the semi-classical transport of free electrons and holes
belongs to
Mathematical Model c
has facts
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
is space-continuous dp "false"^^boolean
description ap "The Scharfetter-Gummel finite volume disretization scheme is the standard numerical method for solving the drift diffusion (aka van Roosbroeck) system describing the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation."@en
wikidata I D ap Q119844 ep
wikidata I D ap Q29367424 ep

Schrödinger Equation (Chebychev Polynomial)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationChebychevPolynomial

Chebchev polynomial scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Schrödinger Equation (Time Dependent) ni
is time-continuous dp "false"^^boolean
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.448136 ep

Schrödinger Equation (Differencing Scheme)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationDifferencingScheme

Differencing scheme (symmetric combination of Euler forward and backward in time) for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Schrödinger Equation (Second Order Differencing) ni
is time-continuous dp "false"^^boolean

Schrödinger Equation (Lie-Trotter)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationLieTrotter

first order (Lie-Trotter) split operator scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Kinetic Operator ni
contains quantity op Quantum Potential Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalized by formulation op Schrödinger Equation (Split Operator) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle=\exp(-i\Delta t\hat{T}/ \hbar)\exp(-i\Delta t\hat{V}/ \hbar)|\psi(t)\rangle + \mathcal{O}(\Delta t)$"^^La Te X ep
in defining formulation dp "$T$, Quantum Kinetic Operator"^^La Te X ep
in defining formulation dp "$V$, Quantum Potential Operator"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
doi I D ap 0021 9991(82)90091 2 ep
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.444501 ep

Schrödinger Equation (Second Order Differencing)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationSecondOrderDifferencing

Second order differencing scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
contains quantity op Planck Constant ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle = |\psi(t-\Delta t)\rangle -2i\Delta t \hat{H}/\hbar |\psi(t)\rangle + \mathcal{O}(\Delta t)^3$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "Essentially a symmetric (and symplectic!) combination of Euler forward and backward methods"@en
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.436072 ep

Schrödinger Equation (Split Operator)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationSplitOperator

Split operator scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Schrödinger Equation (Time Dependent) ni
is time-continuous dp "false"^^boolean

Schrödinger Equation (Strang-Marchuk)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationStrangMarchuk

Second order (Strang-Marchuk) split operator scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Kinetic Operator ni
contains quantity op Quantum Potential Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalized by formulation op Schrödinger Equation (Split Operator) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle=\exp(-i\Delta t\hat{T}/ (2\hbar))\exp(-i\Delta t\hat{V}/ \hbar)\exp(-i\Delta t\hat{T}/ (2\hbar))|\psi(t)\rangle + \mathcal{O}(\Delta t)^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hat{T}$, Quantum Kinetic Operator"^^La Te X ep
in defining formulation dp "$\hat{V}$, Quantum Potential Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi(t)$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
doi I D ap 0021 9991(82)90091 2 ep
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.444501 ep
wikidata I D ap Q25303744 ep

Schrödinger Equation (Time Dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchroedingerEquationTimeDependent

partial differential equation describing how the quantum state of a non-relativistic physical system changes with time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Model (Closed System) ni
contains quantity op Planck Constant ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time ni
generalizes formulation op Classical Hamilton Equations ni
defining formulation dp "$\mathrm{i} \hbar \frac{\partial}{\partial t} | \psi (t) \rangle = \hat{H} | \psi (t) \rangle$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\psi(t)$, Quantum State Vector (Dynamic)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "One of the fundamental postulates of Quantum Mechanics on the time evolution of quantum states."@en
wikidata I D ap Q165498 ep

Schrödinger Equation (Time Independent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationTimeIndependent

eigenvalue equation for the quantum-mechanical Hamiltonian operator, yielding stationary states (wave functions), along with their corresponding energies
belongs to
Mathematical Formulation c
has facts
contains assumption op Time Independence Of Hamiltonian ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Quantum State Vector (Stationary) ni
generalized by formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
defining formulation dp "$\hat H | \psi_n \rangle = E_n | \psi_n \rangle$"^^La Te X ep
in defining formulation dp "$E_n$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\psi_n$, Quantum State Vector (Stationary)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
wikidata I D ap Q25829357 ep

Schrödinger-Newton Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchroedingerNewtonEquation

Coupled equations describing the time evolution in (hybrid) quantum-classical dynamics
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Classical Model ni
contains formulation op Classical Newton Equation ni
contains formulation op Schrödinger Equation (Time Dependent) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean

Second Condition For Positive Solutions In The Multi Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheMultiPopulationSIS_Model

positive solution condition
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains formulation op Between Population Contact Rate Equation ni
contains quantity op Between Population Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha_{ii} \Delta t \leq (\sqrt{1 - a_i} + \sqrt{ \gamma_i \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSIRModelWithBirthsAndDeaths

positive solution condition
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t \leq ( 1 + \sqrt{ \beta \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSISModel

positive solution condition
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t < ( 1 + \sqrt{ \gamma \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIS Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSISModelWithBirthsAndDeaths

positive solution condition
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t < ( 1 + \sqrt{ (\beta + \gamma) \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Eigenvalue of Orthogonal Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondEigenvalueofOrthogonalMatrix

second eigenvalue of an orthogonal matrix
belongs to
Quantity c

SEIR Derivative Relationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SEIRDerivativerelation

derivative relation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op SEIR Derivative Relation ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
defining formulation dp "$\nu^T D \nabla s =\nu^T D \nabla e=\nu^T D \nabla i=\nu^T D \nabla r=0 $"^^La Te X ep
in defining formulation dp "$D$, 'Diffusion Coefficient for SEIR Model'"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$v$, Unit Outer Normal To Domain"^^La Te X ep

Semiconductor Charge Neutralityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorChargeNeutrality

concept of local charge neutrality in semiconductor
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
applies model op Electron Shuttling Model ni
contains constant op Permittivity (Vacuum) ni
contains formulation op Dirichlet Boundary Condition For Electric Potential ni
contains formulation op Laplace Equation For The Electric Potential ni
contains formulation op Neumann Boundary Condition For Electric Potential ni
contains formulation op Periodic Boundary Condition For Electric Potential ni
contains input op Applied External Voltage ni
contains input op Electrode Interfaces ni
contains input op Permittivity (Dielectric) ni
contains output op Electric Potential ni
generalized by task op Semiconductor Thermal Equilibrium ni
description ap "The physical concept of local charge neutrality in semiconductor is characterized by the absence of space charge regions. Hence, the Poisson equation for the electric field potential simplifies to the Laplace equation."@en

Semiconductor Current Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorCurrentVoltage

calculating IV-curves displaying the current voltage charateristics of a semiconductor device
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
contains constant op Permittivity (Vacuum) ni
description ap "In simulations of semiconductor devices, one is usually interested in IV-curves displaying the current voltage charateristics, i.e., the dependence of terminal currents on applied voltages. Therefore, calculating terminal currents accurately is crucial to a successful postprocessing of the simulated field data."@en

Semiconductor Physicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorPhysics

study of semiconductor materials and devices
belongs to
Research Field c
has facts
contains problem op Current Flow in Semiconductor Devices ni
wikidata I D ap Q4483523 ep

Semiconductor Thermal Equilibriumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorThermalEquilibrium

enforce that the drift-diffusion model of a semiconductor is consistent with the thermodynamic equilibrium
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
contains constant op Permittivity (Vacuum) ni
description ap "The goal is to enforce that the drift-diffusion model (aka van Roosbroeck model) of a semiconductor is consistent with the thermodynamic equilibrium, which is a physical state defined by vanishing currents:"@en

Sensitivity Analysis of Complex Kinetic Systemsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SensitivityAnalysisOfComplexKineticSystems

study of uncertainty in complex kinetic systems
belongs to
Computational Task c
has facts
wikidata I D ap Q1889114 ep

Sensory Organni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sensory_Organ

representing a sensory organ
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Sensory Organ Model ni
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
contains quantity op Muscle Spindle Firing Rate ni
defining formulation dp "$$I_\text{spindle} = \sum^{N_\text{spindle}}_{j=1} w_jIa_j\left(\lambda^{j}_{\text{f}}, \dot{\lambda}^{j}_{\text{f}}\right)$$"^^La Te X ep
in defining formulation dp "$Ia_j$, Muscle Spindle Firing Rate"^^La Te X ep
in defining formulation dp "$N$, Amount of spindles"^^La Te X ep
in defining formulation dp "$\dot{\lambda}_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Stretch"^^La Te X ep

Sensory Organ Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SensoryOrganCurrent

sensory organ current
belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni

Sensory Organ Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sensory_Organ_Model

mathematical model to detect macroscopic length change in the muscels and provide the motor neurons with this information.
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is linear dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
doi I D ap gamm.202370009 ep

Simulation of Complex Kinetic Systemsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SimulationOfComplexKineticSystems

study of the time-dependent behavior of complex kinetic systems
belongs to
Computational Task c

Simulation of TEM Imagesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SimulationOfTEMImages

simulating TEM (transmission electron microscopy) images by means of the Darwin Howie Whelan equation
belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
doi I D ap s11082 020 02356 y ep
doi I D ap rspa.2022.0317 ep

Slyke (1914) The mode of action of urease and of enzymes in generalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Slyke_1914_The_mode_of_action_of_urease_and_of_enzymes_in_general

publication
belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
doi I D ap S0021 9258(18)88300 4 ep

Solar System Equations Of Motionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemEquationsOfMotion

mathematical formulation describing the motion of the planets around the sun
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Solar System Model ni
contains quantity op Classical Acceleration ni
contains quantity op Classical Position ni
contains quantity op Gravitational Constant ni
contains quantity op Mass ni
defining formulation dp "$\vec{a}_j = \sum_{i \neq j}^n G \frac{M_i}{|\vec{r}_i - \vec{r}_j|^3} (\vec{r}_i - \vec{r}_j)$"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$a$, Classical Acceleration"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$r$, Classical Position"^^La Te X ep
description ap "The acceleration of a celestial body can be calculated from Newton's Law of Gravitation. Each body attracts each other body, the total acceleration being the sum of all these attractions."@en
wikidata I D ap Q7069658 ep

Solar System Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemMechanics

study of the motion of the planets within our solar system
belongs to
Research Problem c
has facts
contained in field op Celestial Mechanics ni
description ap ""@en
wikidata I D ap Q184274 ep

Solar System Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemModel

classical mechanics model of the sun (fixed) and the 8 planets (moving) as point masses
belongs to
Mathematical Model c
has facts
models op Solar System Mechanics ni
description ap "Neglecting dwarf planets, satellites (e.g. Moon), asteroids, as well as the interaction with other stars or exoplanets. The numerical model of the Solar System consists of a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time."@en
wikidata I D ap Q7069658 ep

Sort Ancient Egyptian Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SortAncientEgyptianObjects

sort ancient egyptian objects
belongs to
Research Problem c
has facts
contained in field op Egyptology ni
modeled by op Object Comparison Model ni

Spatial Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpatialVariable

variable that describes a spatial dimension
belongs to
Quantity c

Species Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeciesTransport

transport of chemical species in some substance
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Diffusion Model ni

Speed Of Lightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeedOfLight

speed of electromagnetic waves in vacuum
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
qudt I D ap Speed Of Light Vacuum ep
wikidata I D ap Q2111 ep

Speed Of Light (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeedOfLightDefinition

speed of electromagnetic waves in vacuum
belongs to
Mathematical Formulation c
has facts
contains quantity op Permeability (Vacuum) ni
contains quantity op Permittivity (Vacuum) ni
contains quantity op Speed Of Light ni
defines op Speed Of Light ni
defining formulation dp "$c \equiv \frac{1}{\sqrt{\epsilon_0 \mu_0}}$"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\mu_0$, Permeability (Vacuum)"^^La Te X ep
in defining formulation dp "$c$, Speed Of Light"^^La Te X ep

Spherical Harmonics Expansion (3D)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SphericalHarmonicsExpansion3D

Representing a function in 3D in terms of spherical harmonics with distance(radius)-dependent coefficients
belongs to
Mathematical Formulation c
has facts
contains quantity op Azimuthal Angle ni
contains quantity op Polar Angle ni
contains quantity op Radius ni
defining formulation dp "$V(r,\theta,\varphi) = \sum_{\ell=0}^\infty\, \sum_{m=-\ell}^\ell C^m_\ell(r)\, Y^m_\ell(\theta,\varphi)$"^^La Te X ep
in defining formulation dp "$\theta$, Azimuthal Angle"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
in defining formulation dp "$r$, Radius"^^La Te X ep

Spin Qbit Shuttlingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpinQbitShuttling

novel functional elements in modular architectures of semiconductor quantum processors
belongs to
Research Problem c
has facts
contained in field op Electromagnetism ni
contained in field op Semiconductor Physics ni
description ap "Spin-qubit shuttles are novel functional elements in modular architectures of semiconductor quantum processors, that have the capability of solving the scalability problem. Such coherent quantum links serve to interconnect different processor units and enable the transfer of quantum information over longer distances across the chip by physical transport of electrons."@en
doi I D ap W I A S. P R E P R I N T.3082 ep

Spreading Curve (Approximate)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ApproximateSpreadingCurve

approximate spreading curve through time
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Spreading Curve (Approximate, Formulation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ApproximateSpreadingCurveFormulation

definition of approximate spreading curve through time
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Number Of Infected Cities ni
contains quantity op Spreading Curve (Approximate) ni
contains quantity op Number of Cities ni
contains quantity op Number of Regions ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Time ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\phi (t\, |\,\sigma , i(0)) \equiv \left( P_m - \int _{0}^t \left. \frac{ds_m(\tau )}{d\tau } \right| _{\sigma , P_m - i(0)} d\tau \right) _{m = 1,\ldots ,N_R}$"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$\frac{ds_m(\tau)}{d\tau}$, Rate of Change of susceptible Cities"^^La Te X ep
in defining formulation dp "$\phi$, Spreading Curve (Approximate)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Spreading of Infectious Diseasesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingOfInfectiousDiseases

spreading of diseases
belongs to
Research Problem c
has facts
contained in field op Epidemiology ni

Spreading Rate (Time-dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingRateTimeDependent

time-dependent spreading rate
belongs to
Quantity c

Spreading Rate (Time-dependent) Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingRateTimeDependentConstraint

constraints applying to time-dependent spreading rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Spreading Rate (Time-dependent) ni
defining formulation dp "$\forall \, t \ge 0,\, 0 \le \alpha (t) < \infty$"^^La Te X ep
in defining formulation dp "$\alpha$, Spreading Rate (Time-dependent)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Spring Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpringConstant

constant of proportionality in Hooke’s law
belongs to
Quantity c
is same as
Force Constant (Harmonic) ni
has facts
description ap "The spring constant is the constant of proportionality in Hooke’s law"@en
wikidata I D ap Q338261 ep

Stability Autonomous Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StabilityAutonomousSystem

asymptotic stability of fixed points of a system of constant coefficient linear differential equations of first order
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Lyapunov Equation Controllability ni
contained as assumption in op Lyapunov Equation Observability ni
contained as assumption in op Lyapunov Generalized Controllability ni
contained as assumption in op Lyapunov Generalized Observability ni
contains quantity op Control System Matrix A ni
defining formulation dp "$\Re(eig(A))$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
description ap "The asymptotic stability of fixed points of a system of constant coefficient linear differential equations of first order (aka linear autonomious system, time-invariant system, $\dot{x}=Ax$) can be analyzed using the eigenvalues of the corresponding matrix."@en
wikidata I D ap Q1756677 ep

Statisticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Statistics

study of the collection, analysis, interpretation, and presentation of data
belongs to
Research Field c
has facts
mardi I D ap Item: Q57236 ep
wikidata I D ap Q12483 ep

Steady State Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SteadyStateAssumption

rate of bound enzyme formation and breakdown is equal
belongs to
Mathematical Formulation c
has facts
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EX}}{dt} = 0$"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Stokes Darcy Coupling Conditionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyCouplingConditions

Coupling free flow of an incompressible fluid (Stokes) to a flow in/through a permeable media (Darcy)
belongs to
Mathematical Formulation c
has facts
contains formulation op Beavers–Joseph-Saffman Condition ni
contains formulation op Continuity of the Normal Mass Flux ni
contains formulation op Continuity of the Normal Stresses ni

Stokes Darcy Equation (Discretized, pv)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyEquationDiscretizedPV

discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Darcy Model (Discretized) ni
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Velocity (Free Flow) ni
defining formulation dp "$\begin{pmatrix} \begin{bmatrix} V & B \\ C & 0 \end{bmatrix} & \begin{bmatrix} B'_1 \\ 0 \end{bmatrix} \\ \begin{bmatrix} C'_1 & 0\end{bmatrix} & D' \end{pmatrix} \begin{pmatrix} \begin{bmatrix} v^{ff} \\ p^{ff} \end{bmatrix} \\ p^{pm} \end{pmatrix} = \begin{pmatrix} \begin{bmatrix} g \\ 0 \end{bmatrix} \\ 0 \end{pmatrix}$"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "Equation (9) from the referenced 2021 arXiv manuscript by Schmalfuss et al.: Discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation, to be solved for every time step"@en
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Equation (Discretized, td)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyEquationDiscretizedTD

discrete model of Stokes-Darcy as a two-domain (td) formulation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Darcy Model (Discretized) ni
contains quantity op Fluid Pressure (Porous Medium) ni
defining formulation dp "$\begin{pmatrix} A' & B' \\ C' & D'\end{pmatrix} \begin{pmatrix} x^{ff} \\ p^{pm} \end{pmatrix} = \begin{pmatrix} b^{ff} \\ 0 \end{pmatrix}$"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "Equation (8) from the referenced 2021 arXiv manuscript by Schmalfuss et al.: Discrete model of Stokes-Darcy as a two-domain (td) formulation, to be solved for every time step"@en
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyModel

free flow model of an incompressible fluid (Stokes model) coupled to a flow in/through a permeable media (Darcy equation)
belongs to
Mathematical Model c
has facts
contains coupling condition op Stokes Darcy Coupling Conditions ni
contains model op Darcy Model ni
contains model op Stokes Model ni
models op Free Flow Coupled to Porous Media Flow ni
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyModelDiscretized

discretized version of a Stokes Darcy model for the incompressible flow in/through porous media
belongs to
Mathematical Model c
has facts
contains model op Darcy Model (Discretized) ni
contains model op Stokes Model (Discretized) ni
discretizes model op Stokes Darcy Model ni
doi I D ap j.camwa.2020.02.012 ep

Stokes Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquation

describes a fluid flow with small advective inertial forces compared to viscous forces
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Model ni
contains quantity op Fluid Density ni
contains quantity op Fluid Kinematic Viscosity (Free Flow) ni
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{\partial v}{\partial t} + \nabla \cdot ( - \nu \left(\nabla v^{ff} + \nabla v^{\mathrm{ff,T}} \right)+ \rho^{-1} p^{ff} I ) &= 0 \\ \nabla \cdot v^{ff} &= 0 \end{align}$"^^La Te X ep
in defining formulation dp "$I$, Identity Map"^^La Te X ep
in defining formulation dp "$\nu$, Fluid Kinematic Viscosity (Free Flow)"^^La Te X ep
in defining formulation dp "$\rho$, Fluid Density"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Stokes equation (also Stokes flow, Stokes law, creeping flow or creeping motion) describes a fluid flow with small advective inertial forces compared to viscous forces, with a low Reynolds number ($Re << 1$). It occurs in situations with very slow fluid velocities, high viscosities, or small flow length scales."@en

Stokes Equation (Euler Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquationEulerBackward

discretizing the Stokes equation by a first-oder backward Euler scheme in time
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Stokes Equation ni
is time-continuous dp "false"^^boolean
description ap "Discretizing the Stokes equation by a first-oder backward Euler scheme in time"@en

Stokes Equation (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquationFiniteVolume

discretizing the Stokes equation by a finite volume scheme in space
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Stokes Equation ni
is space-continuous dp "false"^^boolean
description ap "Discretizing the Stokes equation by a finite volume scheme in space"@en

Stokes Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesModelDiscretized

discretized version of a Stokes model for a fluid flow with small advective inertial forces compared to viscous forces
belongs to
Mathematical Model c
has facts
contains formulation op Stokes Equation (Euler Backward) ni
contains formulation op Stokes Equation (Finite Volume) ni
discretizes model op Stokes Model ni

Stress Free Muscle Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressFreeMuscleLength

length at which a muscle generates minimal or no passive tension
belongs to
Quantity c
has facts
generalized by quantity op Length ni

Stress Free Tendon Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressFreeTendonLength

length of a tendon when it is not under any tension or stress
belongs to
Quantity c
has facts
generalized by quantity op Length ni

Stress Of Crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressOfCrystal

stress of a crystal used in theory of elasticity
belongs to
Quantity c

Stress Tensor (Cauchy)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressTensorCauchy

stress relative to the present configuration
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Stress ni
similar to quantity op Stress Tensor (Piola-Kirchhoff) ni
description ap "In the case of finite deformations, the Cauchy stress tensors express the stress relative to the present configuration. This is in contrast to the Piola–Kirchhoff stress tensor which expresses the stress relative to the reference configuration. For infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical."@en
wikidata I D ap Q13409892 ep

Stress Tensor (Piola-Kirchhoff)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressTensorPiolaKirchhoff

stress relative to the reference configuration
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Stress ni
description ap "In the case of finite deformations, the Piola–Kirchhoff stress tensors express the stress relative to the reference configuration. This is in contrast to the Cauchy stress tensor which expresses the stress relative to the present configuration. For infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical."@en
wikidata I D ap Q9291589 ep

Suan (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Suan_2010_Kinetic_and_reactor_modelling_of_lipases_catalyzed_R_S-1-phenylethanol_resolution

publication
belongs to
Publication c
has facts
surveys op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
description ap "Lee Suan, Chua and Kian Kai, Cheng and Chew Tin, Lee and Sarmid, Mohamad Roji (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolution. Iranica Journal of Energy and Environment, 1 (3). pp. 234-245. ISSN 2079-2115"@en

Subcellular DAE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Subcellular_DAE_System

differential-algebraic equation systems that describes the muscle stress generation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Subcellular Model ni
contains quantity op Ion Current ni
contains quantity op Time ni
contains quantity op Transmembrane Potential ni
defining formulation dp "$\begin{align} \frac{\partial\mathbf{y}}{\partial t} &= G \left(\mathbf{y}, V^{\text{f}}_{\text{m}} \right) \\ I_{\text{ion}} &= I_{\text{ion}} \left(V^{\text{f}}_{\text{m}}, \mathbf{y}\right) \end{align}$"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion current"^^La Te X ep
in defining formulation dp "$V^{\text{f}}_{\text{m}}$, Transmembrane potential"^^La Te X ep
in defining formulation dp "$\mathbf{y}$, Vector of internal state variables"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "A differential-algebraic equation systems that describes the muscle stress generation an a microscopic scale by means of internal state variables and describes the activation of the ion channels."@en

Subcellular Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Subcellular_Model

determines the lumped activation parameter and models the activation of ion channels
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Determines the lumped activation parameter and models the activation of ion channels in response to changes in the muscle fibers transmembrane."@en
doi I D ap gamm.202370009 ep

Substrate 1 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1Concentration

amount of substrate 1 present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
similar to formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} c_{ES_1} - k_{1} c_{E} c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 2 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2Concentration

amount of substrate 2 present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni

Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiOrderedsingleCC

ordinary differential equation describing the concentration over time in an ordered bi bi reaction with a single central complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{2} c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiOrdered

ordinary differential equation describing the concentration over time in an ordered bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} c_{ES_{1}S_{2}} - k_{2} c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiPingPong

ordinary differential equation describing the concentration over time in a ping pong bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-3} c_{E*S_2} - k_{3} c_{E*} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiTheorellChance

ordinary differential equation describing the concentration over time in a Theorell-Chance bi bi reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} c_{EP_2} c_{P_1} - k_{2} c_{ES_1} c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Substrate Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SubstrateConcentration

amount of substrate present in a reaction environment
belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean

Substrate Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SubstrateConcentrationODEUniUni

ordinary differential equation describing the concentration over time in a uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S}}{dt}=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Surface Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SurfaceForceDensity

concept that describes the force per unit area acting on a surface
belongs to
Quantity c

Susceptible Cities ODEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleCitiesODE

ordinary differential equation describing the rate of change of susceptible cities
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
defining formulation dp "$\frac{ds_m(t)}{dt} = -s_m(t) \alpha(t) \sum_{n=1}^{N_R} G_{m,n} i_n(t)$"^^La Te X ep
in defining formulation dp "$G_{m,n}$, Contact Network"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$\alpha(t)$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\frac{ds_m(t)}{dt}$, Rate Of Change Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$i_n(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean

Susceptible Infectious Epidemic Spreading Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousEpidemicSpreadingModel

model for the susceptible infectious epidemic spreading on a network with time-dependent spreading rate.
belongs to
Mathematical Model c
has facts
contains formulation op Susceptible Infectious Epidemic Spreading ODE System ni
contains initial condition op Initial Number Of Infected Cities ni
models op Romanization Spreading in Northern Tunesia ni
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Susceptible Infectious Epidemic Spreading ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousEpidemicSpreadingODESystem

equations describing the spreading in a susceptible infectious epidemic model on a network with time-dependent spreading rate
belongs to
Mathematical Formulation c
has facts
contains formulation op Conservation of City Numbers ni
contains formulation op Susceptible Cities ODE ni
contains quantity op Contact Network ni
contains quantity op Number of Cities ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Region ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{ds_m(t)}{dt} &= -s_m(t) \alpha(t) \sum_{n=1}^{N_R} G_{m,n} i_n(t) \\ i_m(t) &= P_m - s_m(t) \end{align}$"^^La Te X ep
in defining formulation dp "$G_{m,n}$, Contact Network"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$\alpha(t)$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\frac{ds_m(t)}{dt}$, Rate of Change of Susceptible Cities"^^La Te X ep
in defining formulation dp "$i$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean

Susceptible Infectious Removed Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousRemovedModelWithBirthsAndDeaths

discrete-time SIR model with births and deaths
belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptible Infectious Susceptible Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousSusceptibleModelWithBirthsAndDeaths

discrete-time SIS model with births and deaths
belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptiblesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Susceptibles

general quantity for susceptible entities
belongs to
Quantity c
has facts
generalized by op Integer Number (Dimensionless) ni
generalizes op Number Of Susceptible Cities ni
generalizes op Number Of Susceptible Individuals ni
is dimensionless dp "true"^^boolean

Susceptibles At Time Step n +1 in the Discrete Multi Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSIModel

susceptibles in the discrete, multi-population SI model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^{K} \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right)$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n +1 in the Discrete Multi Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSIRModel

susceptibles in the discrete, multi-population SIR model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i\left(1-\sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right)$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n +1 in the Discrete Multi Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSISModel

susceptibles in the discrete, multi-population SIS model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^K \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right) + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The Discrete SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIModel

equation for the susceptibles in the SI model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right)$"^^La Te X ep
in defining formulation dp "$/alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The Discrete SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIRModel

equation for the susceptibles in the SIR model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
discretizes op Continuous Rate of change of Susceptibles in the SIR Model ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in the Discrete SIR Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIRModelWithBirthsAndDeaths

equation for the susceptibles in the SIR model with births and deaths
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n + \beta \Delta t (N - S_n)\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The Discrete SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSISModel

equation for the susceptibles in the SIS model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The Discrete SIS Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSISModelWithBirthsAndDEaths

equation for the susceptibles in the SIS model with births and deaths
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n + \beta \Delta t (N - S_n)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Sylvester (1884) Sur léquations en matrices px = xqni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sylvester_1884_Sur_léquations_en_matrices_px_xq

publication
belongs to
Publication c

Sylvester Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquation

matrix equation, typically used in the field of control theory
belongs to
Mathematical Formulation c
has facts
contained as formulation in op H2 Optimal Approximation ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation ni
generalizes formulation op Sylvester Equation Controllability ni
generalizes formulation op Sylvester Equation Observability ni
invented in op Sylvester (1884) Sur léquations en matrices px = xq ni
defining formulation dp "$AX+XB=C$"^^La Te X ep
in defining formulation dp "$A,B,C$ given matrices"^^La Te X ep
in defining formulation dp "$X$, Unknown Matrix"^^La Te X ep
description ap "Due to the different sizes of A, B, C, the matrix X will be rectangular in general"@en
wikidata I D ap Q3730848 ep

Sylvester Equation Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquationControllability

Sylvester equation for the controllability of a linear control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation Controllability ni
defining formulation dp "$AX + X\tilde{A}^{*} + B\tilde{B}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$X$, Unknown Matrix"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
description ap "Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians."@en

Sylvester Equation Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquationObservability

Sylvester equation for the observability of a linear control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$\tilde{A}Y + YA^{*} - C\tilde{C}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$Υ$, Unknown Matrix"^^La Te X ep
description ap "Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians. However, note the sign change in the CC term."@en

Sylvester Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterGeneralizedControllability

generalized Sylvester equation for the controllability of a bi-linear control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
generalizes formulation op Lyapunov Generalized Controllability ni
generalizes formulation op Sylvester Equation Controllability ni
defining formulation dp "$AX + X\tilde{A}^{*} + \sum_kN_kX\tilde{N}_k^{*} + B\tilde{B}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N (Reduced)"^^La Te X ep
description ap "Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the generalized Lyapunov equations for the calculations of generalized Gramians."@en

Sylvester Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterGeneralizedObservability

generalized Sylvester equation for the observability of a bi-linear control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
generalizes formulation op Sylvester Equation Observability ni
defining formulation dp "$\tilde{A}Y + YA^{*} + \sum_k\tilde{N}_kYN_k^{*} - C\tilde{C}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N (Reduced)"^^La Te X ep
description ap "Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the generalized Lyapunov equations for the calculations of generalized Gramians. However, note the sign change in the CC term."@en

Symmetric Top (Combined)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymmetricTopCombined

modeling a polar oblate or prolate molecule as a rigid symmetric top, interacting with electric fields
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Conditional Quasi-Solvability ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Symmetric Top) ni
models op Molecular Rotation ni
description ap "Modeling a polar oblate (e.g. C6H6) or prolate (e.g. CH3Cl) molecule as a rigid symmetric top, interacting through both its permanent and induced electric dipole moment with electric fields. Note that analytical solutions to the TISE are available, see corresponding Task."@en

Symmetry Analysis In TEM Imagesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymmetryAnalysisTEMImages

symmetry analysis of TEM (transmission electron microscopy) images of crystals with strain
belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
doi I D ap rspa.2022.0317 ep

Symptomatic Infection Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymptomaticInfectionRate

constant representing the symptomatic infection rate
belongs to
Quantity c
has facts
generalized by quantity op Rate ni

Tangential Interaction Force Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Tangential_Interaction_Force_Of_Two_Particles

force component acting tangentially at the contact interface between two particles
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "$\boldsymbol F^T_{ij}=-k^T_{ij}\boldsymbol\xi_{ij}-d^T_{ij}\dot{\boldsymbol \xi}_{ij}$"^^La Te X ep
in defining formulation dp "$\boldsymbol F_{ij}^T$, tangential interaction force"^^La Te X ep
in defining formulation dp "$\boldsymbol \xi'=\boldsymbol x_{C_{ji}}-\boldsymbol x_{C_{ij}}$"^^La Te X ep
in defining formulation dp "$\boldsymbol \xi^T_{ij}=\xi'{ij}-\langle \boldsymbol\xi_{ij}',\boldsymbol n_{ij}\rangle \boldsymbol n_{ij}$"^^La Te X ep
in defining formulation dp "$\boldsymbol t = \boldsymbol \xi_{ij} / \lVert \boldsymbol \xi_{ij}\rVert$, tangential unit vector"^^La Te X ep
in defining formulation dp "$\boldsymbol x_{C_{ij}}$, global contact point between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\dot{\boldsymbol \xi}_{ij}=\langle \boldsymbol v_i-\boldsymbol v_j, \boldsymbol t\rangle \boldsymbol t$, tangential component of relative veloctiy"^^La Te X ep

Temperatureni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Temperature

physical property of matter that quantitatively expresses the common notions of hot and cold
belongs to
Quantity Kind c
has facts
qudt I D ap Temperature ep
wikidata I D ap Q11466 ep

Tendon Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonLength

measurement of the distance from one end of a tendon to the other
belongs to
Quantity c
has facts
generalized by quantity op Length ni

Tendon Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonStrain

stretching or partially tearing a tendon
belongs to
Quantity c
has facts
defined by op Tendon Strain (Definition) ni
description ap "Definition of the tendon strain by length of tendon under stress and stress-free length of tendon"@en

Tendon Strain (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonStrainDefinition

stretching or partially tearing a tendon
belongs to
Mathematical Formulation c
has facts
contains quantity op Stress Free Tendon Length ni
contains quantity op Tendon Length ni
contains quantity op Tendon Strain ni
contains quantity op Time ni
defines op Tendon Strain ni
defining formulation dp "$\epsilon_\text{T}(t) \equiv \frac{\mathcal{l}_\text{T}(t)-\mathcal{l}^{\text{slack}}_\text{T} }{\mathcal{l}^{\text{slack}}_\text{T}$"^^La Te X ep
in defining formulation dp "$\epsilon_{\text{T}$, Tendon Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}^{\text{slack}}_\text{T}$, Stress Free Tendon Length"^^La Te X ep
in defining formulation dp "$l_{\text{T}}$, Tendon Length"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Thermal Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatConductivity

capacity of a material to conduct heat
belongs to
Quantity c
has facts
contained in formulation op Fourier Equation ni
qudt I D ap Thermal Conductivity ep
wikidata I D ap Q487005 ep

Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Time

dimension in which events can be ordered from the past through the present into the future
belongs to
Quantity Kind c
has facts
contained in formulation op Classical Hamilton Equations ni
contained in formulation op Classical Newton Equation ni
contained in formulation op Schrödinger Equation (Time Dependent) ni
qudt I D ap Time ep
wikidata I D ap Q11471 ep

Time Independence Of Hamiltonianni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeIndependenceOfHamiltonian

assuming that the Hamiltonian of a quantum system does not dependend on time explicitly
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Time ni
defining formulation dp "$\frac{\partial}{\partial t}\hat{H}=0$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Time Pointni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimePoint

instant of time
belongs to
Quantity c
has facts
generalized by quantity op Time ni
is dimensionless dp "true"^^boolean

Time Stepni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeStep

incremental time step
belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "Typically used in temporal discretization of evolution equations."@en

Torqueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Torque

tendency of a force to rotate an object
belongs to
Quantity Kind c
has facts
qudt I D ap Torque ep
wikidata I D ap Q48103 ep

Torque Of Particleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Torque_Of_Particle

equation expressing the torque on a particle
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "$\mathbf T_i = (\mathbf x_{a_{ij}} - \mathbf x_i)\times \mathbf F_T$"^^La Te X ep
in defining formulation dp "$\mathbf F_T$, tangential interaction force between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\mathbf T_i$, torque acting on particle $i$"^^La Te X ep
in defining formulation dp "$\mathbf x_i$, position of particle $i$"^^La Te X ep
in defining formulation dp "$\mathbf x_{a_{ij}} = \mathbf x_i + \frac{r_i}{r_i + r_j}(\mathbf x_i - \mathbf x_j)$, actuation point, i.e. mid-point of contact area between particles $i$ and $j$ with radii $r_i$ and $r_j$"^^La Te X ep
description ap "angular velocity needs to be taken into account when transforming the contact point between two particles from local to global coordinates"@en

Total Number Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalNumberOfIndividuals

overall count of people residing within a specific area
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Total Population Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationDensity

number of people living in a given area
belongs to
Quantity c
has facts
description ap "typically expressed as the number of people per square kilometer or square mile"@en

Total Population Density Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationDensityFormulation

represented as a sum of Isotropic Gaussian functions of all provinces
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Isotropic Gaussian Function ni
contains quantity op Total Population Density ni
defining formulation dp "$n(x) \equiv \sum_{\tilde{l}=1}^{\tilde{L}} w_n^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep
in defining formulation dp "$w_n^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Total Population Sizeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationSize

countable quantity representing the number of individuals
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean

Traffic Loadni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TrafficLoad

number of passengers traveling along each edge in the public transportation network
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Transmembrane Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransmembranePotential

difference in electric potential between the interior and the exterior of a biological cell
belongs to
Quantity c
has facts
generalized by quantity op Electric Potential ni
alt Label ap "Membrane Potential"@en
alt Label ap "Membrane Voltage"@en
wikidata I D ap Q389844 ep

Transmission Electron Microscopyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransmissionElectronMicroscopy

uses the propagation of electron waves through magnetic lenses to create images of, e.g., the crystallographic structure of materials down to an atomic scale
belongs to
Research Field c
has facts
description ap "As such, TEM has become an indispensable experimental tool to examine objects in life sciences or in material sciences at nanoscales. See also WIAS annual report 2021"@en
wikidata I D ap Q110779037 ep

Transport Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportEquation

equation that describes the transport of some (extensive) quantity such as mass, energy|heat, momentum, electric charge
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Darcy Equation ni
generalizes formulation op Hooke Law (Linear Elasticity) ni
generalizes formulation op Ohm Equation ni
description ap "There are several (constitutive) equations which describe the transport of matter, or properties of it, in an almost identical way. In every case, in words they read: Flux (density) is proportional to a gradient, where the constant of proportionality is a characteristic of the material. In general, the constant must be replaced by a 2nd rank tensor, to account for directional dependencies of the material."@en
wikidata I D ap Q105560509 ep

Transport Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportModel

constitutive law describing the transport of matter, or properties of it, where the is proportional to a gradient
belongs to
Mathematical Model c
has facts
contains formulation op Transport Equation ni
generalizes model op Charge Transport Model ni
generalizes model op Darcy Model ni
generalizes model op Diffusion Model ni
generalizes model op Heat Conduction Model ni
description ap "There are several (constitutive) equations which describe the transport of matter, or properties of it, in an almost identical way. In every case, in words they read: Flux (density) is proportional to a gradient, where the constant of proportionality is a characteristic of the material. In general, the constant must be replaced by a 2nd rank tensor, to account for directional dependencies of the material."@en

Transport of Matterni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportOfMatter

transport of matter or of properties thereof
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
generalizes problem op Charge Transport ni
generalizes problem op Flow in Porous Media ni
generalizes problem op Heat Transport ni
generalizes problem op Species Transport ni
modeled by op Transport Model ni

Transport Routeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportRoute

route on which goods, persons or data are transported
belongs to
Quantity c
has facts
generalizes quantity op PTN Line ni
wikidata I D ap "https://www.wikidata.org/wiki/Q1297806"

Transportation Planningni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportationPlanning

planning of transportation networks and traffic
belongs to
Research Field c
has facts
studied in op Gattermann (2017) Line pool generation ni
wikidata I D ap "https://www.wikidata.org/wiki/Q1034047"

Turn Over Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TurnOverTime

time between two events
belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "Time between two events, e.g. minimal time between services of lines in public transport"@en

Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UncompetitiveInhibitionConstantUniUniReactionReversibleInhibition

constant for the uncompetitive inhibition in an uni uni reaction
belongs to
Quantity c
has facts
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean

Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UncompetitiveInhibitionConstantUniUniReactionReversibleInhibitionDefinition

constant for the uncompetitive inhibition in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
contains quantity op Reaction Rate Constant ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defines op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$K_{iu} \equiv \frac{k_{-4}}{k_4} $"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
description ap "definition of the uncompetitive inhibition constant in an uni uni reaction with reversible inhibition"@en

Uni Uni Reactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReaction

reaction catalyzed by an enzyme in which one substrate and one product is involved
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Uni Uni Reaction (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionODEModel

uni uni reaction model
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Uni Uni Reaction ODE System ni
contains initial condition op Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Uni Uni Reaction ni
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "Ordinary differential equations for the rates of change of all chemical species (substrate, enzyme, enzyme-substrate complex, product) in an Uni Uni reaction. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step."@en

Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

uni uni reaction Dixon model without product and competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

uni uni reaction Eadie Hofstee model without product and competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

uni uni reaction Hanes Woolf model without Product and competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

uni uni reaction Lineweaver Burk model without product and competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and competitive partial Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

uni uni reaction Dixon model without product and mixed complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

uni uni reaction Eadie Hofstee model without product and mixed complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

uni uni reaction Hanes Woolf model without product and mixed complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

uni uni reaction Lineweaver Burk model without product and mixed complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and mixed complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedPartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and mixed partial Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

uni uni reaction Dixon model without product and non-competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

uni uni reaction Eadie-Hofstee model without product and non-competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

uni uni reaction Hanes Woolf model without product and non-competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

uni uni reaction Lineweaver Burk model without product and non-competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and non-competitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Dixon model without product and non-competitive partial Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionODESystem

system of ordinary differential equations describing an uni uni reaction over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme Concentration ODE (Uni Uni Reaction) ni
contains formulation op Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction) ni
contains formulation op Product Concentration ODE (Uni Uni Reaction) ni
contains formulation op Substrate Concentration ODE (Uni Uni Reaction) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S}}{dt}&=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES} \\ \frac{dc_{P}}{dt}&=k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P} \\ \frac{dc_{E}}{dt}&=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}+k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P} \\ \frac{dc_{ES}}{dt}&=k_{1}*c_{E}*c_{S}-k_{-1}*c_{ES}-k_{2}*c_{ES}+k_{-2}*c_{E}*c_{P} \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{P}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{S}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

uni uni reaction Dixon model without product and uncompetitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

uni uni reaction Eadie Hofstee model without product and uncompetitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

uni uni reaction Hanes Woolf model without product and uncompetitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

uni uni reaction Lineweaver Burk model without product and uncompetitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and uncompetitive complete Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

uni uni reaction Michaelis Menten model without product and uncompetitive partial Inhibition via the steady state assumption
belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Uni Uni Reaction with Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithCompetitiveCompleteInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme may bind an inhibitor (I) to form an enzyme-inhibitor complex (EI) with rates $k_{3}$ and $k_{-3}$."@en

Uni Uni Reaction with Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithCompetitivePartialInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex product is formed with rate $k_{2}$. Properly this is a mixed partial inhibition in which the inhibitor does not affect the turnover rate,"@en

Uni Uni Reaction with Mixed Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithMixedCompleteInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex no product formation is possible, the inhibition is thus complete."@en

Uni Uni Reaction with Mixed Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithMixedPartialInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex product is formed with rate $k_{6}$."@en

Uni Uni Reaction with Non-Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithNonCompetitiveCompleteInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. In the non-competitive case: $k_{3} = k_{4}$, $k_{-3} = k_{-4}$, $k_{5} = k_{1}$ and $k_{-5} = k_{-1}$. The enzyme-inhibitor-substrate complex cannot form product, the inhibition is thus complete."@en

Uni Uni Reaction with Non-Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithNonCompetitivePartialInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. In the non-competitive case: $k_{3} = k_{4}$, $k_{-3} = k_{-4}$, $k_{5} = k_{1}$ and $k_{-5} = k_{-1}$. The enzyme-inhibitor-substrate complex can form product with rate $k_{6}."@en

Uni Uni Reaction with Reversible Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithReversibleCompleteInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
description ap "Uni Uni Reaction with reversible inhibition. The enzyme-inhibitor-substrate complex (EIS) cannot form product, the inhibition is thus complete."@en

Uni Uni Reaction with Reversible Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithReversiblePartialInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
description ap "Uni Uni Reaction with reversible inhibition. The enzyme-inhibitor-substrate complex (EIS) can form product, the inhibition is thus partial."@en

Uni Uni Reaction with Uncompetitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithUncompetitiveCompleteInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor-substrate complex (EIS) with rates $k_{4}$ and $k_{-4}$. The enzyme-inhibitor-substrate complex cannot form product, the inhibition is thus complete."@en

Uni Uni Reaction with Uncompetitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithUncompetitivePartialInhibition

uni uni reaction with inhibition
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni
description ap "Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor-substrate complex (EIS) with rates $k_{4}$ and $k_{-4}$. The enzyme-inhibitor-substrate complex can form product with rate $k_{6}$."@en

Uniform Gravitational Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniformGravitationalAcceleration

assuming that the gravitational constant remains unchanged from the beginning to the end of a trajectory, e.g. a free fall
belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Radius ni
contains quantity op Free Fall Height ni
defining formulation dp "$h \approx r$"^^La Te X ep
in defining formulation dp "$h$, Free Fall Height"^^La Te X ep
in defining formulation dp "$r$, Earth Radius"^^La Te X ep
description ap "This is a very good approximation for an apple falling from a tree, but not for celestial mechanics where the inverse-square law of the gravitational field must be taken into account."@en

Unit Normal Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnitNormalVector

vector that is normal to some surface (typically an interface), with unit length
belongs to
Quantity c
has facts
wikidata I D ap Q91093255 ep

Unit Tangent Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnitTangentVector

vector that is tangential to a curve or surface at a given point, with unit length
belongs to
Quantity c
has facts
wikidata I D ap Q106041131 ep

Unknown Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnknownMatrix

unknown matrix, to be found
belongs to
Quantity c

Upper-Triangular Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UpperTriangularMatrix

matrix with all elements below the main diagonal equal to zero
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean

Vanishing Air Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VanishingAirDensity

in the limit of vanishing air density, physical bodies will move like in vacuum, e.g. free fall models
belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Air ni
defining formulation dp "$\rho\rightarrow 0$"^^La Te X ep
in defining formulation dp "$\rho$, Density of Air"^^La Te X ep

Vanishing Drag Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VanishingDragCoefficient

in the limit of vanishing drag coefficient, physical bodies will move like in vacuum, e.g. free fall models
belongs to
Mathematical Formulation c
has facts
contains quantity op Drag Coefficient ni
defining formulation dp "$C_D\rightarrow 0$"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep

Varianceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Variance

expectation of the squared deviation of a random variable from its mean
belongs to
Quantity Kind c
has facts
wikidata I D ap Q175199 ep

Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Velocity

rate of change of the position of an object as a function of time, and the direction of that change
belongs to
Quantity Kind c
has facts
qudt I D ap Velocity ep
wikidata I D ap Q11465 ep

Vibration Frequency (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationFrequencyAnharmonic

frequency of oscillation in systems that deviate from the ideal harmonic oscillator model
belongs to
Quantity c
has facts
generalizes quantity op Vibration Frequency (Harmonic) ni
wikidata I D ap Q545228 ep

Vibration Frequency (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationFrequencyHarmonic

harmonic frequency of vibration, e.g. of a molecule
belongs to
Quantity c
has facts
generalized by quantity op Frequency ni
wikidata I D ap Q677864 ep

Vibrational Frequency Shift (1st Order)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationalFrequencyShift1stOrder

frequency shift of molecular vibrations caused by interaction with surrounding particles from 1st order non-degenerate perturbation theory
belongs to
Mathematical Formulation c
has facts
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Quantum Eigen Energy ni
defining formulation dp "$E_{1,r}^{(1)}-E_{0,r}^{(1)}= \frac{1}{2} \frac{\partial^2U}{\partial q_r^2}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "The interpretation is quite straight-forward: Effectively, the intermolecular potential changes the effective force constant of a vibrational normal mode."@en

Vibrational Frequency Shift (2nd Order)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationalFrequencyShift2ndOrder

frequency shift of molecular vibrations caused by interaction with surrounding particles from 2nd order non-degenerate perturbation theory
belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$E_{1,r}^{(2)}-E_{0,r}^{(2)}= \frac{1}{2} \frac{\phi_{rrs}}{\omega_s} \frac{\partial U}{\partial q_s}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency Harmonic"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "The interpretation is based on the coupling of different vibrational normal modes, mediated by the cubic anharmonicity of the intramolecular force field."@en

Viscosityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Viscosity

resistance of a fluid to shear deformation
belongs to
Quantity Kind c
has facts
qudt I D ap Viscosity ep
wikidata I D ap Q128709 ep

Viscous Dissipation Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ViscousDissipationPotential

describes the conversion of mechanical energy into internal energy due to the viscosity of a fluid
belongs to
Quantity c

Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricVoltage

difference in electric potential between two points (indicated in volt)
belongs to
Quantity Kind c
has facts
qudt I D ap Voltage ep
wikidata I D ap Q25428 ep

Wave Vector of an Electronni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WaveVectorElectron

vector pointing in the direction of propagation of a wave and whose magnitude is equal to the wavenumber
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
description ap "Vector pointing in the direction of a wave and whose magnitude is equal to the wavenumber. In quantum mechanics/condensed matter physics, a wave vector is the quotient of the momentum vektor of particles or quasi particles and the reduced Planck constant"@en
wikidata I D ap Q657009 ep

Weber (2022) The Mathematics of Comparing Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Weber_2022_The_Mathematics_of_Comparing_Objects

publication
belongs to
Publication c
has facts
invents op Object Comparison Model ni
arxiv I D ap 2201.07032v2 ep
doi I D ap ar Xiv.2201.07032 ep

Weight Factorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WeightFactor

maximum between the data and the standard deviation for specific region
belongs to
Quantity c
has facts
defined by op Weight Factor (Definition) ni
is dimensionless dp "true"^^boolean

Weight Factor (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WeightFactorDefinition

maximum between the data and the standard deviation for specific region
belongs to
Mathematical Formulation c
has facts
contains quantity op Romanized Cities Vector ni
contains quantity op Weight Factor ni
defines op Weight Factor ni
defining formulation dp "$C_{m,t_i} \equiv \max \{ \omega _{m,t_i}, STD(\omega _{m,\bullet })\}$"^^La Te X ep
in defining formulation dp "$C$, Weight Factor"
in defining formulation dp "$\omega$, Romanized Cities Vector"
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

White Noiseni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WhiteNoise

delta-correlated stationary Gaussian process with zero-mean
belongs to
Quantity c
has facts
description ap "Delta-correlated stationary Gaussian process with zero-mean, i.e., a random signal with equal intensity at all frequencies, yielding a constant power spectral density."@en
wikidata I D ap Q381287 ep

Wiener Processni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WienerProcess

stochastic process generalizing Brownian motion
belongs to
Quantity c
has facts
similar to quantity op White Noise ni
description ap "A stochastic process generalizing Brownian motion, used to represent the integral of a white noise Gaussian process,"@en
wikidata I D ap Q1056809 ep

Young Modulusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#YoungModulus

mechanical property that measures stiffness of a solid material
belongs to
Quantity c
has facts
alt Label ap "Elastic modulus"@en
alt Label ap "Modulus of elasticity"@en
alt Label ap "Young's modulus"@en
wikidata I D ap Q2091584 ep

Young Modulus (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#YoungModulusDefinition

mechanical property that measures stiffness of a solid material
belongs to
Mathematical Formulation c
has facts
contains quantity op Linear Strain ni
contains quantity op Normal Stress ni
contains quantity op Young Modulus ni
defines op Young Modulus ni
defining formulation dp "$E \equiv \frac{\sigma}{\varepsilon}$"^^La Te X ep
in defining formulation dp "$E$, Young Modulus"^^La Te X ep
in defining formulation dp "$\sigma$, Normal Stress"^^La Te X ep
in defining formulation dp "$\varepsilon$, Linear Strain"^^La Te X ep

Legend back to ToC

c: Classes
op: Object Properties
dp: Data Properties
ni: Named Individuals
ep: External Properties

References back to ToC

Acknowledgments back to ToC

The work has been funded by the DFG (German Research Foundation), project number 460135501, NFDI 29/1 “MaRDI – Mathematische Forschungsdateninitiative”.

The authors would like to thank Silvio Peroni for developing LODE, a Live OWL Documentation Environment, which is used for representing the Cross Referencing Section of this document and Daniel Garijo for developing Widoco, the program used to create the template used in this documentation.